F(x)=-2x^2+53x

Solution for F(x)=-2x^2+53x equation:

(F)=-2F^2+53F

We move all terms to the left:

(F)-(-2F^2+53F)=0

We get rid of parentheses

2F^2-53F+F=0

We add all the numbers together, and all the variables

2F^2-52F=0

a = 2; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·2·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*2}=\frac{0}{4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*2}=\frac{104}{4}
=26
$