-2p^2+12p=6p-7p^2

Solution for -2p^2+12p=6p-7p^2 equation:

-2p^2+12p=6p-7p^2

We move all terms to the left:

-2p^2+12p-(6p-7p^2)=0

We get rid of parentheses

-2p^2+7p^2-6p+12p=0

We add all the numbers together, and all the variables

5p^2+6p=0

a = 5; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·5·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*5}=\frac{-12}{10}
=-1+1/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*5}=\frac{0}{10}
=0
$