9x^2-18x-36=9

Solution for 9x^2-18x-36=9 equation:

9x^2-18x-36=9

We move all terms to the left:

9x^2-18x-36-(9)=0

We add all the numbers together, and all the variables

9x^2-18x-45=0

a = 9; b = -18; c = -45;
Δ = b2-4ac
Δ = -182-4·9·(-45)
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{6}}{2*9}=\frac{18-18\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{6}}{2*9}=\frac{18+18\sqrt{6}}{18}
$