P=-x^2+28x-90

Solution for P=-x^2+28x-90 equation:

=-P^2+28P-90

We move all terms to the left:

-(-P^2+28P-90)=0

We get rid of parentheses

P^2-28P+90=0

a = 1; b = -28; c = +90;
Δ = b2-4ac
Δ = -282-4·1·90
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{106}}{2*1}=\frac{28-2\sqrt{106}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{106}}{2*1}=\frac{28+2\sqrt{106}}{2}
$