F(x)=4x2-5

Solution for F(x)=4x2-5 equation:

(F)=4F^2-5

We move all terms to the left:

(F)-(4F^2-5)=0

We get rid of parentheses

-4F^2+F+5=0

a = -4; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-4)·5
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*-4}=\frac{8}{-8}
=-1
$