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

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

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

We move all terms to the left:

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

We get rid of parentheses

-5F^2+F+8F+2=0

We add all the numbers together, and all the variables

-5F^2+9F+2=0

a = -5; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-5)·2
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*-5}=\frac{-20}{-10}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*-5}=\frac{2}{-10}
=-1/5
$