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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-0.5x^2+40x-600=0

a = -0.5; b = 40; c = -600;
Δ = b2-4ac
Δ = 402-4·(-0.5)·(-600)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20}{2*-0.5}=\frac{-60}{-1}
=+60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20}{2*-0.5}=\frac{-20}{-1}
=+20
$