9x^2=72x+1

Solution for 9x^2=72x+1 equation:

9x^2=72x+1

We move all terms to the left:

9x^2-(72x+1)=0

We get rid of parentheses

9x^2-72x-1=0

a = 9; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·9·(-1)
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{145}}{2*9}=\frac{72-6\sqrt{145}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{145}}{2*9}=\frac{72+6\sqrt{145}}{18}
$