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

Solution for F(x)=-8x^2-8x+96 equation:

(F)=-8F^2-8F+96

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8F^2+9F-96=0

a = 8; b = 9; c = -96;
Δ = b2-4ac
Δ = 92-4·8·(-96)
Δ = 3153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{3153}}{2*8}=\frac{-9-\sqrt{3153}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{3153}}{2*8}=\frac{-9+\sqrt{3153}}{16}
$