3x(4x-2)=2(6x-3)

Solution for 3x(4x-2)=2(6x-3) equation:

3x(4x-2)=2(6x-3)

We move all terms to the left:

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

We multiply parentheses

12x^2-6x-(2(6x-3))=0


We calculate terms in parentheses: -(2(6x-3)), so:

2(6x-3)

We multiply parentheses

12x-6

Back to the equation:

-(12x-6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2-18x+6=0

a = 12; b = -18; c = +6;
Δ = b2-4ac
Δ = -182-4·12·6
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*12}=\frac{12}{24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*12}=\frac{24}{24}
=1
$