-3x(6x-1)=6x-9

Solution for -3x(6x-1)=6x-9 equation:

-3x(6x-1)=6x-9

We move all terms to the left:

-3x(6x-1)-(6x-9)=0

We multiply parentheses

-18x^2+3x-(6x-9)=0

We get rid of parentheses

-18x^2+3x-6x+9=0

We add all the numbers together, and all the variables

-18x^2-3x+9=0

a = -18; b = -3; c = +9;
Δ = b2-4ac
Δ = -32-4·(-18)·9
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{73}}{2*-18}=\frac{3-3\sqrt{73}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{73}}{2*-18}=\frac{3+3\sqrt{73}}{-36}
$