F(x)=2x^2-24x+64

Solution for F(x)=2x^2-24x+64 equation:

(F)=2F^2-24F+64

We move all terms to the left:

(F)-(2F^2-24F+64)=0

We get rid of parentheses

-2F^2+F+24F-64=0

We add all the numbers together, and all the variables

-2F^2+25F-64=0

a = -2; b = 25; c = -64;
Δ = b2-4ac
Δ = 252-4·(-2)·(-64)
Δ = 113
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{-(25)-\sqrt{113}}{2*-2}=\frac{-25-\sqrt{113}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{113}}{2*-2}=\frac{-25+\sqrt{113}}{-4}
$