Question

solve for x. write both solutions, separated by a comma. 6x² + 5x - 6 = 0 enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $6x^2 + 5x - 6 = 0$, we have $a=6$, $b=5$, $c=-6$.

Step2: Apply quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:

$$ x = \frac{-5 \pm \sqrt{5^2 - 4(6)(-6)}}{2(6)} $$

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{25 + 144} = \sqrt{169} = 13$

Step4: Solve for both x values

First solution:
$x = \frac{-5 + 13}{12} = \frac{8}{12} = \frac{2}{3}$
Second solution:
$x = \frac{-5 - 13}{12} = \frac{-18}{12} = -\frac{3}{2}$

Answer:

$\frac{2}{3}, -\frac{3}{2}$