F(x)=8x^2+32X+2

Solution for F(x)=8x^2+32X+2 equation:

(F)=8F^2+32F+2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8F^2-31F-2=0

a = -8; b = -31; c = -2;
Δ = b2-4ac
Δ = -312-4·(-8)·(-2)
Δ = 897
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{-(-31)-\sqrt{897}}{2*-8}=\frac{31-\sqrt{897}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{897}}{2*-8}=\frac{31+\sqrt{897}}{-16}
$