(3x-3)(2/3)=9

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

(3x-3)(2/3)=9

We move all terms to the left:

(3x-3)(2/3)-(9)=0

We add all the numbers together, and all the variables

(3x-3)(+2/3)-9=0

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-33=0

a = 6; b = 0; c = -33;
Δ = b2-4ac
Δ = 02-4·6·(-33)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{22}}{2*6}=\frac{0-6\sqrt{22}}{12}
=-\frac{6\sqrt{22}}{12}
=-\frac{\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{22}}{2*6}=\frac{0+6\sqrt{22}}{12}
=\frac{6\sqrt{22}}{12}
=\frac{\sqrt{22}}{2}
$