9p=-2p^2-2p-5

Solution for 9p=-2p^2-2p-5 equation:

9p=-2p^2-2p-5

We move all terms to the left:

9p-(-2p^2-2p-5)=0

We get rid of parentheses

2p^2+2p+9p+5=0

We add all the numbers together, and all the variables

2p^2+11p+5=0

a = 2; b = 11; c = +5;
Δ = b2-4ac
Δ = 112-4·2·5
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*2}=\frac{-20}{4}
=-5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*2}=\frac{-2}{4}
=-1/2
$