7-3p^2=-2+6p

Solution for 7-3p^2=-2+6p equation:

7-3p^2=-2+6p

We move all terms to the left:

7-3p^2-(-2+6p)=0

We add all the numbers together, and all the variables

-3p^2-(6p-2)+7=0

We get rid of parentheses

-3p^2-6p+2+7=0

We add all the numbers together, and all the variables

-3p^2-6p+9=0

a = -3; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-3)·9
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{-(-6)-12}{2*-3}=\frac{-6}{-6}
=1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*-3}=\frac{18}{-6}
=-3
$