3x-1=1/2x-4

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

3x-1=1/2x-4

We move all terms to the left:

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


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

3x-1/2x+4-1=0

We multiply all the terms by the denominator


3x*2x+4*2x-1*2x-1=0

Wy multiply elements

6x^2+8x-2x-1=0

We add all the numbers together, and all the variables

6x^2+6x-1=0

a = 6; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·6·(-1)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*6}=\frac{-6-2\sqrt{15}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*6}=\frac{-6+2\sqrt{15}}{12}
$