3(p^2)-3=4(p^2)-52

Solution for 3(p^2)-3=4(p^2)-52 equation:

3(p^2)-3=4(p^2)-52

We move all terms to the left:

3(p^2)-3-(4(p^2)-52)=0

We get rid of parentheses

3p^2-4p^2+52-3=0

We add all the numbers together, and all the variables

-1p^2+49=0

a = -1; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-1)·49
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*-1}=\frac{-14}{-2}
=+7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*-1}=\frac{14}{-2}
=-7
$