30(p^2-1)=11

Solution for 30(p^2-1)=11 equation:

30(p^2-1)=11

We move all terms to the left:

30(p^2-1)-(11)=0

We multiply parentheses

30p^2-30-11=0

We add all the numbers together, and all the variables

30p^2-41=0

a = 30; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·30·(-41)
Δ = 4920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4920}=\sqrt{4*1230}=\sqrt{4}*\sqrt{1230}=2\sqrt{1230}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1230}}{2*30}=\frac{0-2\sqrt{1230}}{60}
=-\frac{2\sqrt{1230}}{60}
=-\frac{\sqrt{1230}}{30}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1230}}{2*30}=\frac{0+2\sqrt{1230}}{60}
=\frac{2\sqrt{1230}}{60}
=\frac{\sqrt{1230}}{30}
$