300=50x+300-90x-0.5x^2

Solution for 300=50x+300-90x-0.5x^2 equation:

300=50x+300-90x-0.5x^2

We move all terms to the left:

300-(50x+300-90x-0.5x^2)=0

We get rid of parentheses

0.5x^2-50x+90x-300+300=0

We add all the numbers together, and all the variables

0.5x^2+40x=0

a = 0.5; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·0.5·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*0.5}=\frac{-80}{1}
=-80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*0.5}=\frac{0}{1}
=0
$