F(5x^2)=8(5x)-1

Solution for F(5x^2)=8(5x)-1 equation:

(5F^2)=8(5F)-1

We move all terms to the left:

(5F^2)-(8(5F)-1)=0

We get rid of parentheses

5F^2-85F+1=0

a = 5; b = -85; c = +1;
Δ = b2-4ac
Δ = -852-4·5·1
Δ = 7205
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{-(-85)-\sqrt{7205}}{2*5}=\frac{85-\sqrt{7205}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{7205}}{2*5}=\frac{85+\sqrt{7205}}{10}
$