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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2+11F-8=0

a = -2; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·(-2)·(-8)
Δ = 57
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{-(11)-\sqrt{57}}{2*-2}=\frac{-11-\sqrt{57}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{57}}{2*-2}=\frac{-11+\sqrt{57}}{-4}
$