-9p=-2p^2-8

Solution for -9p=-2p^2-8 equation:

-9p=-2p^2-8

We move all terms to the left:

-9p-(-2p^2-8)=0

We get rid of parentheses

2p^2-9p+8=0

a = 2; b = -9; c = +8;
Δ = b2-4ac
Δ = -92-4·2·8
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{17}}{2*2}=\frac{9-\sqrt{17}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{17}}{2*2}=\frac{9+\sqrt{17}}{4}
$