12p^2+20p=8p^2+56

Solution for 12p^2+20p=8p^2+56 equation:

12p^2+20p=8p^2+56

We move all terms to the left:

12p^2+20p-(8p^2+56)=0

We get rid of parentheses

12p^2-8p^2+20p-56=0

We add all the numbers together, and all the variables

4p^2+20p-56=0

a = 4; b = 20; c = -56;
Δ = b2-4ac
Δ = 202-4·4·(-56)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-36}{2*4}=\frac{-56}{8}
=-7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+36}{2*4}=\frac{16}{8}
=2
$