(95x-0.5x^2)-(55x=300)=300

Solution for (95x-0.5x^2)-(55x=300)=300 equation:

(95x-0.5x^2)-(55x=300)=300

We move all terms to the left:

(95x-0.5x^2)-(55x-(300))=0

We get rid of parentheses

-0.5x^2+95x-55x+300=0

We add all the numbers together, and all the variables

-0.5x^2+40x+300=0

a = -0.5; b = 40; c = +300;
Δ = b2-4ac
Δ = 402-4·(-0.5)·300
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{22}}{2*-0.5}=\frac{-40-10\sqrt{22}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{22}}{2*-0.5}=\frac{-40+10\sqrt{22}}{-1}
$