F(x)=-5+8x^2

Solution for F(x)=-5+8x^2 equation:

(F)=-5+8F^2

We move all terms to the left:

(F)-(-5+8F^2)=0

We get rid of parentheses

-8F^2+F+5=0

a = -8; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-8)·5
Δ = 161
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{161}}{2*-8}=\frac{-1-\sqrt{161}}{-16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{161}}{2*-8}=\frac{-1+\sqrt{161}}{-16}
$