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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2x(2x-1)), so:

2x(2x-1)

We multiply parentheses

4x^2-2x

Back to the equation:

-(4x^2-2x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -4; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-4)·9
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*-4}=\frac{-2-2\sqrt{37}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*-4}=\frac{-2+2\sqrt{37}}{-8}
$