2x-3x(2x-1)=3-4x

Solution for 2x-3x(2x-1)=3-4x equation:

2x-3x(2x-1)=3-4x

We move all terms to the left:

2x-3x(2x-1)-(3-4x)=0

We add all the numbers together, and all the variables

2x-3x(2x-1)-(-4x+3)=0

We multiply parentheses

-6x^2+2x+3x-(-4x+3)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -6; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·(-6)·(-3)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-6}=\frac{-6}{-12}
=1/2
$