(45x+300)-(85x-0.5x^2)=50

Solution for (45x+300)-(85x-0.5x^2)=50 equation:

(45x+300)-(85x-0.5x^2)=50

We move all terms to the left:

(45x+300)-(85x-0.5x^2)-(50)=0

We get rid of parentheses

0.5x^2-85x+45x+300-50=0

We add all the numbers together, and all the variables

0.5x^2-40x+250=0

a = 0.5; b = -40; c = +250;
Δ = b2-4ac
Δ = -402-4·0.5·250
Δ = 1100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{11}}{2*0.5}=\frac{40-10\sqrt{11}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{11}}{2*0.5}=\frac{40+10\sqrt{11}}{1}
$