X^2-2000x=-60000

Solution for X^2-2000x=-60000 equation:

X^2-2000X=-60000

We move all terms to the left:

X^2-2000X-(-60000)=0

We add all the numbers together, and all the variables

X^2-2000X+60000=0

a = 1; b = -2000; c = +60000;
Δ = b2-4ac
Δ = -20002-4·1·60000
Δ = 3760000
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:

$\sqrt{\Delta}=\sqrt{3760000}=\sqrt{40000*94}=\sqrt{40000}*\sqrt{94}=200\sqrt{94}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2000)-200\sqrt{94}}{2*1}=\frac{2000-200\sqrt{94}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2000)+200\sqrt{94}}{2*1}=\frac{2000+200\sqrt{94}}{2}
$