p^2=-19p-88

Solution for p^2=-19p-88 equation:

p^2=-19p-88

We move all terms to the left:

p^2-(-19p-88)=0

We get rid of parentheses

p^2+19p+88=0

a = 1; b = 19; c = +88;
Δ = b2-4ac
Δ = 192-4·1·88
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3}{2*1}=\frac{-22}{2}
=-11
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3}{2*1}=\frac{-16}{2}
=-8
$