85000=39999x^2+500x

Solution for 85000=39999x^2+500x equation:

85000=39999x^2+500x

We move all terms to the left:

85000-(39999x^2+500x)=0

We get rid of parentheses

-39999x^2-500x+85000=0

a = -39999; b = -500; c = +85000;
Δ = b2-4ac
Δ = -5002-4·(-39999)·85000
Δ = 13599910000
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:

$\sqrt{\Delta}=\sqrt{13599910000}=\sqrt{10000*1359991}=\sqrt{10000}*\sqrt{1359991}=100\sqrt{1359991}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-100\sqrt{1359991}}{2*-39999}=\frac{500-100\sqrt{1359991}}{-79998}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+100\sqrt{1359991}}{2*-39999}=\frac{500+100\sqrt{1359991}}{-79998}
$