9x^2-12x=11

Solution for 9x^2-12x=11 equation:

9x^2-12x=11

We move all terms to the left:

9x^2-12x-(11)=0

a = 9; b = -12; c = -11;
Δ = b2-4ac
Δ = -122-4·9·(-11)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{15}}{2*9}=\frac{12-6\sqrt{15}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{15}}{2*9}=\frac{12+6\sqrt{15}}{18}
$