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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-3))!=0

x∈R


We multiply parentheses

6x-(4(1/2x-3))-2=0

We multiply all the terms by the denominator


6x*2x-2*2x-3))-(4(1-3))=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

6x*2x-2*2x=0

Wy multiply elements

12x^2-4x=0

a = 12; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·12·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*12}=\frac{8}{24}
=1/3
$