F(x)=-x^2+60x

Solution for F(x)=-x^2+60x equation:

(F)=-F^2+60F

We move all terms to the left:

(F)-(-F^2+60F)=0

We get rid of parentheses

F^2-60F+F=0

We add all the numbers together, and all the variables

F^2-59F=0

a = 1; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·1·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*1}=\frac{118}{2}
=59
$