45(p^2-1)=56

Solution for 45(p^2-1)=56 equation:

45(p^2-1)=56

We move all terms to the left:

45(p^2-1)-(56)=0

We multiply parentheses

45p^2-45-56=0

We add all the numbers together, and all the variables

45p^2-101=0

a = 45; b = 0; c = -101;
Δ = b2-4ac
Δ = 02-4·45·(-101)
Δ = 18180
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:

$\sqrt{\Delta}=\sqrt{18180}=\sqrt{36*505}=\sqrt{36}*\sqrt{505}=6\sqrt{505}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{505}}{2*45}=\frac{0-6\sqrt{505}}{90}
=-\frac{6\sqrt{505}}{90}
=-\frac{\sqrt{505}}{15}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{505}}{2*45}=\frac{0+6\sqrt{505}}{90}
=\frac{6\sqrt{505}}{90}
=\frac{\sqrt{505}}{15}
$