81p^2-3=78

Solution for 81p^2-3=78 equation:

81p^2-3=78

We move all terms to the left:

81p^2-3-(78)=0

We add all the numbers together, and all the variables

81p^2-81=0

a = 81; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·81·(-81)
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-162}{2*81}=\frac{-162}{162}
=-1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+162}{2*81}=\frac{162}{162}
=1
$