P=-10x2+160x-588

Solution for P=-10x2+160x-588 equation:

=-10P^2+160P-588

We move all terms to the left:

-(-10P^2+160P-588)=0

We get rid of parentheses

10P^2-160P+588=0

a = 10; b = -160; c = +588;
Δ = b2-4ac
Δ = -1602-4·10·588
Δ = 2080
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:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-4\sqrt{130}}{2*10}=\frac{160-4\sqrt{130}}{20}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+4\sqrt{130}}{2*10}=\frac{160+4\sqrt{130}}{20}
$