F(x)=-50x^2+300x

Solution for F(x)=-50x^2+300x equation:

(F)=-50F^2+300F

We move all terms to the left:

(F)-(-50F^2+300F)=0

We get rid of parentheses

50F^2-300F+F=0

We add all the numbers together, and all the variables

50F^2-299F=0

a = 50; b = -299; c = 0;
Δ = b2-4ac
Δ = -2992-4·50·0
Δ = 89401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{89401}=299$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-299)-299}{2*50}=\frac{0}{100}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-299)+299}{2*50}=\frac{598}{100}
=5+49/50
$