F(x)=2x2-4x

Solution for F(x)=2x2-4x equation:

(F)=2F^2-4F

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2+5F=0

a = -2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-2}=\frac{0}{-4}
=0
$