P=-5x*x+400x-3000

Solution for P=-5x*x+400x-3000 equation:

=-5P*P+400P-3000

We move all terms to the left:

-(-5P*P+400P-3000)=0

We add all the numbers together, and all the variables

-(400P-5P*P-3000)=0

We get rid of parentheses

-400P+5P*P+3000=0

Wy multiply elements

5P^2-400P+3000=0

a = 5; b = -400; c = +3000;
Δ = b2-4ac
Δ = -4002-4·5·3000
Δ = 100000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{100000}=\sqrt{10000*10}=\sqrt{10000}*\sqrt{10}=100\sqrt{10}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-100\sqrt{10}}{2*5}=\frac{400-100\sqrt{10}}{10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+100\sqrt{10}}{2*5}=\frac{400+100\sqrt{10}}{10}
$