p(p+9)=11p+99

Solution for p(p+9)=11p+99 equation:

p(p+9)=11p+99

We move all terms to the left:

p(p+9)-(11p+99)=0

We multiply parentheses

p^2+9p-(11p+99)=0

We get rid of parentheses

p^2+9p-11p-99=0

We add all the numbers together, and all the variables

p^2-2p-99=0

a = 1; b = -2; c = -99;
Δ = b2-4ac
Δ = -22-4·1·(-99)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-20}{2*1}=\frac{-18}{2}
=-9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+20}{2*1}=\frac{22}{2}
=11
$