F(x)=5x^2-4x-2

Solution for F(x)=5x^2-4x-2 equation:

(F)=5F^2-4F-2

We move all terms to the left:

(F)-(5F^2-4F-2)=0

We get rid of parentheses

-5F^2+F+4F+2=0

We add all the numbers together, and all the variables

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

a = -5; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-5)·2
Δ = 65
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{-(5)-\sqrt{65}}{2*-5}=\frac{-5-\sqrt{65}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*-5}=\frac{-5+\sqrt{65}}{-10}
$