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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

6x-(3x(2x-1))-3=0


We calculate terms in parentheses: -(3x(2x-1)), so:

3x(2x-1)

We multiply parentheses

6x^2-3x

Back to the equation:

-(6x^2-3x)


We get rid of parentheses

-6x^2+6x+3x-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
$