3x-3(x-3)=2x(2x-1+2x-1)

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

3x-3(x-3)=2x(2x-1+2x-1)

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x-3(x-3)-(2x(4x-2))=0

We multiply parentheses

3x-3x-(2x(4x-2))+9=0


We calculate terms in parentheses: -(2x(4x-2)), so:

2x(4x-2)

We multiply parentheses

8x^2-4x

Back to the equation:

-(8x^2-4x)


We add all the numbers together, and all the variables

-(8x^2-4x)+9=0

We get rid of parentheses

-8x^2+4x+9=0

a = -8; b = 4; c = +9;
Δ = b2-4ac
Δ = 42-4·(-8)·9
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{19}}{2*-8}=\frac{-4-4\sqrt{19}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{19}}{2*-8}=\frac{-4+4\sqrt{19}}{-16}
$