Question

solve for x. write both solutions, separated by a comma.
6x² - x - 15 = 0
enter the correct answer.

Explanation:

Step1: Use quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=6$, $b=-1$, $c=-15$.

Step2: Calculate discriminant

$\Delta = (-1)^2 - 4\times6\times(-15) = 1 + 360 = 361$

Step3: Compute square root of discriminant

$\sqrt{\Delta} = \sqrt{361} = 19$

Step4: Find first solution

$x_1 = \frac{-(-1)+19}{2\times6} = \frac{20}{12} = \frac{5}{3}$

Step5: Find second solution

$x_2 = \frac{-(-1)-19}{2\times6} = \frac{-18}{12} = -\frac{3}{2}$

Answer:

$\frac{5}{3}, -\frac{3}{2}$