Question

solve for x. write both solutions, separated by a comma.
8x² - 2x - 15 = 0
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=8$, $b=-2$, $c=-15$

Step2: Apply quadratic formula

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

Step3: Calculate discriminant

$\sqrt{b^2-4ac}=\sqrt{(-2)^2-4(8)(-15)}=\sqrt{4+480}=\sqrt{484}=22$

Step4: Compute two solutions

$x_1=\frac{-(-2)+22}{2(8)}=\frac{24}{16}=\frac{3}{2}$
$x_2=\frac{-(-2)-22}{2(8)}=\frac{-20}{16}=-\frac{5}{4}$

Answer:

$\frac{3}{2}, -\frac{5}{4}$