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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x(x-1)-(5x-3)=0

We multiply parentheses

3x^2-3x-(5x-3)=0

We get rid of parentheses

3x^2-3x-5x+3=0

We add all the numbers together, and all the variables

3x^2-8x+3=0

a = 3; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·3·3
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{7}}{2*3}=\frac{8-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{7}}{2*3}=\frac{8+2\sqrt{7}}{6}
$