F(x)=10x^2-8x-2

Solution for F(x)=10x^2-8x-2 equation:

(F)=10F^2-8F-2

We move all terms to the left:

(F)-(10F^2-8F-2)=0

We get rid of parentheses

-10F^2+F+8F+2=0

We add all the numbers together, and all the variables

-10F^2+9F+2=0

a = -10; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-10)·2
Δ = 161
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{-(9)-\sqrt{161}}{2*-10}=\frac{-9-\sqrt{161}}{-20}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{161}}{2*-10}=\frac{-9+\sqrt{161}}{-20}
$