p^2=-19p-90

Solution for p^2=-19p-90 equation:

p^2=-19p-90

We move all terms to the left:

p^2-(-19p-90)=0

We get rid of parentheses

p^2+19p+90=0

a = 1; b = 19; c = +90;
Δ = b2-4ac
Δ = 192-4·1·90
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-1}{2*1}=\frac{-20}{2}
=-10
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+1}{2*1}=\frac{-18}{2}
=-9
$