x^2-1=72x

Solution for x^2-1=72x equation:

x^2-1=72x

We move all terms to the left:

x^2-1-(72x)=0

a = 1; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·1·(-1)
Δ = 5188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5188}=\sqrt{4*1297}=\sqrt{4}*\sqrt{1297}=2\sqrt{1297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1297}}{2*1}=\frac{72-2\sqrt{1297}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1297}}{2*1}=\frac{72+2\sqrt{1297}}{2}
$