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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5F^2+3F-1=0

a = 5; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·5·(-1)
Δ = 29
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{-(3)-\sqrt{29}}{2*5}=\frac{-3-\sqrt{29}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*5}=\frac{-3+\sqrt{29}}{10}
$