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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8F^2-1F+3=0

a = -8; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-8)·3
Δ = 97
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{-(-1)-\sqrt{97}}{2*-8}=\frac{1-\sqrt{97}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-8}=\frac{1+\sqrt{97}}{-16}
$