72(x2-x)=1

Solution for 72(x2-x)=1 equation:

72(x2-x)=1

We move all terms to the left:

72(x2-x)-(1)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

72x^2-72x-1=0

a = 72; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·72·(-1)
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{38}}{2*72}=\frac{72-12\sqrt{38}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{38}}{2*72}=\frac{72+12\sqrt{38}}{144}
$