F(x)=8x^2+16x+3

Solution for F(x)=8x^2+16x+3 equation:

(F)=8F^2+16F+3

We move all terms to the left:

(F)-(8F^2+16F+3)=0

We get rid of parentheses

-8F^2+F-16F-3=0

We add all the numbers together, and all the variables

-8F^2-15F-3=0

a = -8; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·(-8)·(-3)
Δ = 129
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{-(-15)-\sqrt{129}}{2*-8}=\frac{15-\sqrt{129}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{129}}{2*-8}=\frac{15+\sqrt{129}}{-16}
$