10000+5000x=500x^2

Solution for 10000+5000x=500x^2 equation:

10000+5000x=500x^2

We move all terms to the left:

10000+5000x-(500x^2)=0

determiningTheFunctionDomain
-500x^2+5000x+10000=0

a = -500; b = 5000; c = +10000;
Δ = b2-4ac
Δ = 50002-4·(-500)·10000
Δ = 45000000
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:

$\sqrt{\Delta}=\sqrt{45000000}=\sqrt{9000000*5}=\sqrt{9000000}*\sqrt{5}=3000\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-3000\sqrt{5}}{2*-500}=\frac{-5000-3000\sqrt{5}}{-1000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+3000\sqrt{5}}{2*-500}=\frac{-5000+3000\sqrt{5}}{-1000}
$