F(x)=5x^2-1

Solution for F(x)=5x^2-1 equation:

(F)=5F^2-1

We move all terms to the left:

(F)-(5F^2-1)=0

We get rid of parentheses

-5F^2+F+1=0

a = -5; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-5)·1
Δ = 21
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{21}}{2*-5}=\frac{-1-\sqrt{21}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*-5}=\frac{-1+\sqrt{21}}{-10}
$