9x^2-6x-1=11

Solution for 9x^2-6x-1=11 equation:

9x^2-6x-1=11

We move all terms to the left:

9x^2-6x-1-(11)=0

We add all the numbers together, and all the variables

9x^2-6x-12=0

a = 9; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·9·(-12)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{13}}{2*9}=\frac{6-6\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{13}}{2*9}=\frac{6+6\sqrt{13}}{18}
$