Kalkulator notacji naukowej

Rozwiązywanie Równań

Rozwiązuj równania liniowe, kwadratowe i z jedną zmienną z krokami, deltą, resztą i sprawdzeniem przez podstawienie.

RównanieMetodaRozwiązanie

Rozwiązuj równania liniowe, kwadratowe i z jedną zmienną z krokami, deltą, resztą i sprawdzeniem przez podstawienie.

Gotowe

Rozwiązuj równania liniowe, kwadratowe i z jedną zmienną z krokami, deltą, resztą i sprawdzeniem przez podstawienie.

Krok po kroku

Podsumowanie

Rozwiązania: x = 4
Równanie: 2x + 3 = 11

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Konwerter

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Rozwiązywanie Równań

Rozwiązuj równania liniowe, kwadratowe i z jedną zmienną z krokami, deltą, resztą i sprawdzeniem przez podstawienie.

What is an equation?

An equation states that two mathematical expressions have the same value. Solving means finding every variable value that keeps the equality true. In 2x + 5 = 11, subtract 5 from both sides to get 2x = 6, then divide by 2, so x = 3. For x^2 - 5x + 6 = 0, factoring or the quadratic formula gives x = 2 or x = 3.

How do you use the equation solver?

Enter exactly one equals sign and choose the variable, usually x. The input can contain arithmetic, parentheses, powers, roots, logarithms and trigonometric functions. For exact algebraic answers, linear and quadratic equations are recognized first; broader expressions are scanned over the selected interval.

After solving, read the method label. Linear exact solve means inverse operations isolated the variable. Quadratic exact solve means the discriminant was checked. Numerical root search means sign changes were located in the interval. The residual tells how close the computed root makes left minus right equal zero.

Which equation examples should you check?

Required examples: 2x + 5 = 11 gives x = 3. The quadratic x^2 - 5x + 6 = 0 gives x = 2 or x = 3. A fraction equation such as x/2 + 1 = 4 clears denominators first, giving x + 2 = 8 and x = 6.

What equation mistakes should you avoid?

Common mistakes include changing only one side of an equation, distributing parentheses incorrectly, losing a negative sign, dividing by zero, using too narrow a numerical search interval and forgetting to verify by substitution. Always apply the same operation to both sides and check the result in the original equation.

Equation Solving Rules and Reference Tables

These tables show the common algebra moves behind the solver. Each rule keeps the equality balanced: whatever is added, subtracted, multiplied or divided on one side must be applied to the other side as well.

Addition and subtraction equations

For one-step additive equations, undo addition with subtraction and undo subtraction with addition. This isolates the variable without changing equality.

Equation	Inverse operation	Step result	Solution
x + 7 = 12	Subtract 7 from both sides	x = 12 - 7	x = 5
x - 4 = 9	Add 4 to both sides	x = 9 + 4	x = 13

Multiplication and division equations

For multiplicative equations, divide by the coefficient or multiply by the denominator. The divisor must be nonzero.

Equation	Inverse operation	Step result	Solution
4x = 28	Divide both sides by 4	x = 28 / 4	x = 7
x/3 = 5	Multiply both sides by 3	x = 5 x 3	x = 15

Two-step equations

Two-step equations usually remove the constant first, then divide by the coefficient of the variable.

Equation	Step 1	Step 2	Solution
3x + 5 = 20	Subtract 5: 3x = 15	Divide by 3	x = 5
2x - 7 = 9	Add 7: 2x = 16	Divide by 2	x = 8

Variable on both sides

When the variable appears on both sides, collect variable terms on one side and constants on the other before dividing.

Equation	Collect variables	Collect constants	Solution
5x = 3x + 14	5x - 3x = 14	Divide by 2	x = 7
6x - 2 = 4x + 8	2x = 10	Divide by 2	x = 5

Equations with parentheses

Parentheses are handled with the distributive property before collecting like terms.

Equation	Distribute	Collect terms	Solution
2(x + 3) = 10	2x + 6 = 10	2x = 4	x = 2
3(2x - 1) = 15	6x - 3 = 15	6x = 18	x = 3

Equations with fractions

Fractions are cleared by multiplying every term by the least common denominator, then solving the simpler equation.

Equation	Denominator	Cleared equation	Solution
x/2 + 1 = 4	LCD = 2	x + 2 = 8	x = 6
x/3 - x/6 = 2	LCD = 6	2x - x = 12	x = 12

Checking solutions

Substitution checks whether each proposed answer makes the original left side equal the original right side.

Equation	Simplified	Candidate	Check
2x + 5 = 11	2x = 6	x = 3	2(3) + 5 = 11
x^2 - 5x + 6 = 0	x = 2, 3	two roots	0 = 0

Proces

Przebieg obliczeń

Enter equation

Choose variable

Solve

Verify

The solver parses both sides, moves terms into a single function, tries exact linear or quadratic solving, then uses numerical search when needed.

Formaty wejściowe

Obsługiwane formaty

Input type	Example
Linear	2x + 5 = 11
Quadratic	x^2 - 5x + 6 = 0
Fraction	x/2 + 1 = 4
Function	sin(x) = 0.5

Odniesienie

Popularne stałe naukowe

Wróć do kalkulatora

Concept	Meaning	Example	Use
Variable	unknown value	x	solve target
Root	solution value	x = 3	answer
Residual	left minus right	0	verification

Pytania

Pytania o kalkulator

How do you solve linear equations?

Use inverse operations to isolate the variable. Add or subtract constants first, then divide by the variable coefficient. Apply every operation to both sides.

How does the quadratic formula calculator step work?

The solver identifies a quadratic form, calculates b^2 - 4ac, then uses the quadratic formula when real roots exist.

Can it solve a system of equations?

This page focuses on one-variable equations. A two-variable system needs a dedicated system solver or algebraic substitution outside this calculator.

How do you solve for x?

Move all x terms to one side, constants to the other side, then divide by the coefficient of x. Substitute the answer back to verify.

What does the discriminant show?

The discriminant b^2 - 4ac shows whether a quadratic has two real roots, one repeated real root, or no real roots.