3p^2-120=-9p

Solution for 3p^2-120=-9p equation:

3p^2-120=-9p

We move all terms to the left:

3p^2-120-(-9p)=0

We get rid of parentheses

3p^2+9p-120=0

a = 3; b = 9; c = -120;
Δ = b2-4ac
Δ = 92-4·3·(-120)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*3}=\frac{-48}{6}
=-8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*3}=\frac{30}{6}
=5
$