6(x^2-x)=9

Solution for 6(x^2-x)=9 equation:

6(x^2-x)=9

We move all terms to the left:

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

We multiply parentheses

6x^2-6x-9=0

a = 6; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·6·(-9)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{7}}{2*6}=\frac{6-6\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{7}}{2*6}=\frac{6+6\sqrt{7}}{12}
$