300=110x-0.5x^2+60x+500

Solution for 300=110x-0.5x^2+60x+500 equation:

300=110x-0.5x^2+60x+500

We move all terms to the left:

300-(110x-0.5x^2+60x+500)=0

We get rid of parentheses

0.5x^2-110x-60x-500+300=0

We add all the numbers together, and all the variables

0.5x^2-170x-200=0

a = 0.5; b = -170; c = -200;
Δ = b2-4ac
Δ = -1702-4·0.5·(-200)
Δ = 29300
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:

$\sqrt{\Delta}=\sqrt{29300}=\sqrt{100*293}=\sqrt{100}*\sqrt{293}=10\sqrt{293}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-10\sqrt{293}}{2*0.5}=\frac{170-10\sqrt{293}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+10\sqrt{293}}{2*0.5}=\frac{170+10\sqrt{293}}{1}
$