-0.5x^2+400x-6000=30000

Solution for -0.5x^2+400x-6000=30000 equation:

-0.5x^2+400x-6000=30000

We move all terms to the left:

-0.5x^2+400x-6000-(30000)=0

We add all the numbers together, and all the variables

-0.5x^2+400x-36000=0

a = -0.5; b = 400; c = -36000;
Δ = b2-4ac
Δ = 4002-4·(-0.5)·(-36000)
Δ = 88000
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:

$\sqrt{\Delta}=\sqrt{88000}=\sqrt{1600*55}=\sqrt{1600}*\sqrt{55}=40\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-40\sqrt{55}}{2*-0.5}=\frac{-400-40\sqrt{55}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+40\sqrt{55}}{2*-0.5}=\frac{-400+40\sqrt{55}}{-1}
$