5000x=2x^2-15000

Solution for 5000x=2x^2-15000 equation:

5000x=2x^2-15000

We move all terms to the left:

5000x-(2x^2-15000)=0

We get rid of parentheses

-2x^2+5000x+15000=0

a = -2; b = 5000; c = +15000;
Δ = b2-4ac
Δ = 50002-4·(-2)·15000
Δ = 25120000
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:

$\sqrt{\Delta}=\sqrt{25120000}=\sqrt{160000*157}=\sqrt{160000}*\sqrt{157}=400\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-400\sqrt{157}}{2*-2}=\frac{-5000-400\sqrt{157}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+400\sqrt{157}}{2*-2}=\frac{-5000+400\sqrt{157}}{-4}
$