9u^2-3u=6

Solution for 9u^2-3u=6 equation:

9u^2-3u=6

We move all terms to the left:

9u^2-3u-(6)=0

a = 9; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·9·(-6)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*9}=\frac{-12}{18}
=-2/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*9}=\frac{18}{18}
=1
$