p^2-9=-33p+5-4p^2

Solution for p^2-9=-33p+5-4p^2 equation:

p^2-9=-33p+5-4p^2

We move all terms to the left:

p^2-9-(-33p+5-4p^2)=0

We get rid of parentheses

p^2+4p^2+33p-5-9=0

We add all the numbers together, and all the variables

5p^2+33p-14=0

a = 5; b = 33; c = -14;
Δ = b2-4ac
Δ = 332-4·5·(-14)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-37}{2*5}=\frac{-70}{10}
=-7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+37}{2*5}=\frac{4}{10}
=2/5
$