F(x)=8x^2-32x-4

Solution for F(x)=8x^2-32x-4 equation:

(F)=8F^2-32F-4

We move all terms to the left:

(F)-(8F^2-32F-4)=0

We get rid of parentheses

-8F^2+F+32F+4=0

We add all the numbers together, and all the variables

-8F^2+33F+4=0

a = -8; b = 33; c = +4;
Δ = b2-4ac
Δ = 332-4·(-8)·4
Δ = 1217
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{-(33)-\sqrt{1217}}{2*-8}=\frac{-33-\sqrt{1217}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1217}}{2*-8}=\frac{-33+\sqrt{1217}}{-16}
$