2000=x^2-30x+220

Solution for 2000=x^2-30x+220 equation:

2000=x^2-30x+220

We move all terms to the left:

2000-(x^2-30x+220)=0

We get rid of parentheses

-x^2+30x-220+2000=0

We add all the numbers together, and all the variables

-1x^2+30x+1780=0

a = -1; b = 30; c = +1780;
Δ = b2-4ac
Δ = 302-4·(-1)·1780
Δ = 8020
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:

$\sqrt{\Delta}=\sqrt{8020}=\sqrt{4*2005}=\sqrt{4}*\sqrt{2005}=2\sqrt{2005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{2005}}{2*-1}=\frac{-30-2\sqrt{2005}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{2005}}{2*-1}=\frac{-30+2\sqrt{2005}}{-2}
$