x^2-300x=3000

Solution for x^2-300x=3000 equation:

x^2-300x=3000

We move all terms to the left:

x^2-300x-(3000)=0

a = 1; b = -300; c = -3000;
Δ = b2-4ac
Δ = -3002-4·1·(-3000)
Δ = 102000
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:

$\sqrt{\Delta}=\sqrt{102000}=\sqrt{400*255}=\sqrt{400}*\sqrt{255}=20\sqrt{255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-20\sqrt{255}}{2*1}=\frac{300-20\sqrt{255}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+20\sqrt{255}}{2*1}=\frac{300+20\sqrt{255}}{2}
$