F(x)=-5x2+100x

Solution for F(x)=-5x2+100x equation:

(F)=-5F^2+100F

We move all terms to the left:

(F)-(-5F^2+100F)=0

We get rid of parentheses

5F^2-100F+F=0

We add all the numbers together, and all the variables

5F^2-99F=0

a = 5; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·5·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*5}=\frac{0}{10}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*5}=\frac{198}{10}
=19+4/5
$