x^2-300x=-15000

Solution for x^2-300x=-15000 equation:

x^2-300x=-15000

We move all terms to the left:

x^2-300x-(-15000)=0

We add all the numbers together, and all the variables

x^2-300x+15000=0

a = 1; b = -300; c = +15000;
Δ = b2-4ac
Δ = -3002-4·1·15000
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-100\sqrt{3}}{2*1}=\frac{300-100\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+100\sqrt{3}}{2*1}=\frac{300+100\sqrt{3}}{2}
$