5p^2-6p=3(2p^2+2p)

Solution for 5p^2-6p=3(2p^2+2p) equation:

5p^2-6p=3(2p^2+2p)

We move all terms to the left:

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


We calculate terms in parentheses: -(3(2p^2+2p)), so:

3(2p^2+2p)

We multiply parentheses

6p^2+6p

Back to the equation:

-(6p^2+6p)


We get rid of parentheses

5p^2-6p^2-6p-6p=0

We add all the numbers together, and all the variables

-1p^2-12p=0

a = -1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-1)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-1}=\frac{0}{-2}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-1}=\frac{24}{-2}
=-12
$