F(x-1)=5x^2-7x-1

Solution for F(x-1)=5x^2-7x-1 equation:

(F-1)=5F^2-7F-1

We move all terms to the left:

(F-1)-(5F^2-7F-1)=0

We get rid of parentheses

-5F^2+F+7F-1+1=0

We add all the numbers together, and all the variables

-5F^2+8F=0

a = -5; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-5)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-5}=\frac{-16}{-10}
=1+3/5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-5}=\frac{0}{-10}
=0
$