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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4F^2-7F+4=0

a = -4; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-4)·4
Δ = 113
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{-(-7)-\sqrt{113}}{2*-4}=\frac{7-\sqrt{113}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{113}}{2*-4}=\frac{7+\sqrt{113}}{-8}
$