9x^2-9x=36

Solution for 9x^2-9x=36 equation:

9x^2-9x=36

We move all terms to the left:

9x^2-9x-(36)=0

a = 9; b = -9; c = -36;
Δ = b2-4ac
Δ = -92-4·9·(-36)
Δ = 1377
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:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{17}}{2*9}=\frac{9-9\sqrt{17}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{17}}{2*9}=\frac{9+9\sqrt{17}}{18}
$