100x-0.5x^2=60x+30

Solution for 100x-0.5x^2=60x+30 equation:

100x-0.5x^2=60x+30

We move all terms to the left:

100x-0.5x^2-(60x+30)=0

We get rid of parentheses

-0.5x^2+100x-60x-30=0

We add all the numbers together, and all the variables

-0.5x^2+40x-30=0

a = -0.5; b = 40; c = -30;
Δ = b2-4ac
Δ = 402-4·(-0.5)·(-30)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{385}}{2*-0.5}=\frac{-40-2\sqrt{385}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{385}}{2*-0.5}=\frac{-40+2\sqrt{385}}{-1}
$