Algebra • Step-by-Step

Solve 2x² - 7x + 3 = 0 with Steps

Find the roots of 2x² - 7x + 3 = 0 step by step. Factor into (2x - 1)(x - 3) = 0 to get x = 0.5 and x = 3.

Problem Statement

2x^2 - 7x + 3 = 0

Final Result

x_1 = \frac{1}{2}, \quad x_2 = 3

Formula Required: Quadratic Formula

√25 = 5. x = (7 + 5)/4 = 3, and x = (7 - 5)/4 = 0.5.

x = \frac{7 \pm \sqrt{(-7)^2 - 4(2)(3)}}{4} = \frac{7 \pm \sqrt{25}}{4}

5 Steps

Write the equation in standard quadratic form $ax^2 + bx + c = 0$.

2x^2 - 7x + 3 = 0

Apply the $ac$ factoring method: find two numbers that multiply to $ac = (2)(3) = 6$ and add up to $b = -7$.

(-1) \times (-6) = 6, \quad (-1) + (-6) = -7

Split the middle term $-7x$ into $-1x + (-6)x$ and factor by grouping.

2x^2 - 1x - 6x + 3 = 0 \implies (2x - 1)(x - 3) = 0

Set each factor equal to zero and solve for $x$.

(2x - 1) = 0 \implies x_1 = 0.5 \quad \text{or} \quad (x - 3) = 0 \implies x_2 = 3

Verify each root by substituting back into the original equation.

\text{Check } x = 0.5: \; 2(0.5)^2 - 7(0.5) + 3 = 0.5 - 3.5 + 3 = 0 \;\checkmark \\[6pt] \text{Check } x = 3: \; 2(3)^2 - 7(3) + 3 = 18 - 21 + 3 = 0 \;\checkmark

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

x = 3 and x = 1/2.