x=0.01x^2+60x-500

Solution for x=0.01x^2+60x-500 equation:

x=0.01x^2+60x-500

We move all terms to the left:

x-(0.01x^2+60x-500)=0

We get rid of parentheses

-0.01x^2+x-60x+500=0

We add all the numbers together, and all the variables

-0.01x^2-59x+500=0

a = -0.01; b = -59; c = +500;
Δ = b2-4ac
Δ = -592-4·(-0.01)·500
Δ = 3501
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:

$\sqrt{\Delta}=\sqrt{3501}=\sqrt{9*389}=\sqrt{9}*\sqrt{389}=3\sqrt{389}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-3\sqrt{389}}{2*-0.01}=\frac{59-3\sqrt{389}}{-0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+3\sqrt{389}}{2*-0.01}=\frac{59+3\sqrt{389}}{-0.02}
$