96=8x+2x^2

Solution for 96=8x+2x^2 equation:

96=8x+2x^2

We move all terms to the left:

96-(8x+2x^2)=0

We get rid of parentheses

-2x^2-8x+96=0

a = -2; b = -8; c = +96;
Δ = b2-4ac
Δ = -82-4·(-2)·96
Δ = 832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{13}}{2*-2}=\frac{8-8\sqrt{13}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{13}}{2*-2}=\frac{8+8\sqrt{13}}{-4}
$