6p^2-4p-30=3p^2+5p

Solution for 6p^2-4p-30=3p^2+5p equation:

6p^2-4p-30=3p^2+5p

We move all terms to the left:

6p^2-4p-30-(3p^2+5p)=0

We get rid of parentheses

6p^2-3p^2-4p-5p-30=0

We add all the numbers together, and all the variables

3p^2-9p-30=0

a = 3; b = -9; c = -30;
Δ = b2-4ac
Δ = -92-4·3·(-30)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-21}{2*3}=\frac{-12}{6}
=-2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*3}=\frac{30}{6}
=5
$