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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply parentheses

-4x^2+2x+12x-3x-6=0

We add all the numbers together, and all the variables

-4x^2+11x-6=0

a = -4; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·(-4)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*-4}=\frac{-6}{-8}
=3/4
$