3x(2x-1)=6-9x

Solution for 3x(2x-1)=6-9x equation:

3x(2x-1)=6-9x

We move all terms to the left:

3x(2x-1)-(6-9x)=0

We add all the numbers together, and all the variables

3x(2x-1)-(-9x+6)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+6x-6=0

a = 6; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·6·(-6)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*6}=\frac{-6-6\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*6}=\frac{-6+6\sqrt{5}}{12}
$