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

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

(F)=8F^2+4F

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8F^2-3F=0

a = -8; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-8)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-8}=\frac{0}{-16}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-8}=\frac{6}{-16}
=-3/8
$