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 add all the numbers together, and all the variables

-(-5F^2+1)+F=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}
$