-30x^2+1200x+4000=5000

Solution for -30x^2+1200x+4000=5000 equation:

-30x^2+1200x+4000=5000

We move all terms to the left:

-30x^2+1200x+4000-(5000)=0

We add all the numbers together, and all the variables

-30x^2+1200x-1000=0

a = -30; b = 1200; c = -1000;
Δ = b2-4ac
Δ = 12002-4·(-30)·(-1000)
Δ = 1320000
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:

$\sqrt{\Delta}=\sqrt{1320000}=\sqrt{40000*33}=\sqrt{40000}*\sqrt{33}=200\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-200\sqrt{33}}{2*-30}=\frac{-1200-200\sqrt{33}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+200\sqrt{33}}{2*-30}=\frac{-1200+200\sqrt{33}}{-60}
$