P(x)=x^2+9x-90

Solution for P(x)=x^2+9x-90 equation:

(P)=P^2+9P-90

We move all terms to the left:

(P)-(P^2+9P-90)=0

We get rid of parentheses

-P^2+P-9P+90=0

We add all the numbers together, and all the variables

-1P^2-8P+90=0

a = -1; b = -8; c = +90;
Δ = b2-4ac
Δ = -82-4·(-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{-(-8)-2\sqrt{106}}{2*-1}=\frac{8-2\sqrt{106}}{-2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{106}}{2*-1}=\frac{8+2\sqrt{106}}{-2}
$