4000=-5x^2+400x-2550

Solution for 4000=-5x^2+400x-2550 equation:

4000=-5x^2+400x-2550

We move all terms to the left:

4000-(-5x^2+400x-2550)=0

We get rid of parentheses

5x^2-400x+2550+4000=0

We add all the numbers together, and all the variables

5x^2-400x+6550=0

a = 5; b = -400; c = +6550;
Δ = b2-4ac
Δ = -4002-4·5·6550
Δ = 29000
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:

$\sqrt{\Delta}=\sqrt{29000}=\sqrt{100*290}=\sqrt{100}*\sqrt{290}=10\sqrt{290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-10\sqrt{290}}{2*5}=\frac{400-10\sqrt{290}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+10\sqrt{290}}{2*5}=\frac{400+10\sqrt{290}}{10}
$