5p^2=-18-33p

Solution for 5p^2=-18-33p equation:

5p^2=-18-33p

We move all terms to the left:

5p^2-(-18-33p)=0

We add all the numbers together, and all the variables

5p^2-(-33p-18)=0

We get rid of parentheses

5p^2+33p+18=0

a = 5; b = 33; c = +18;
Δ = b2-4ac
Δ = 332-4·5·18
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-27}{2*5}=\frac{-60}{10}
=-6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+27}{2*5}=\frac{-6}{10}
=-3/5
$