9u^2-9u-2=0

Solution for 9u^2-9u-2=0 equation:

9u^2-9u-2=0

a = 9; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·9·(-2)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{17}}{2*9}=\frac{9-3\sqrt{17}}{18}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{17}}{2*9}=\frac{9+3\sqrt{17}}{18}
$