9x^2-6x-1=10

Solution for 9x^2-6x-1=10 equation:

9x^2-6x-1=10

We move all terms to the left:

9x^2-6x-1-(10)=0

We add all the numbers together, and all the variables

9x^2-6x-11=0

a = 9; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·9·(-11)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{3}}{2*9}=\frac{6-12\sqrt{3}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{3}}{2*9}=\frac{6+12\sqrt{3}}{18}
$