2x-1=3/2x-12

Solution for 2x-1=3/2x-12 equation:

2x-1=3/2x-12

We move all terms to the left:

2x-1-(3/2x-12)=0


Domain of the equation: 2x-12)!=0

x∈R


We get rid of parentheses

2x-3/2x+12-1=0

We multiply all the terms by the denominator


2x*2x+12*2x-1*2x-3=0

Wy multiply elements

4x^2+24x-2x-3=0

We add all the numbers together, and all the variables

4x^2+22x-3=0

a = 4; b = 22; c = -3;
Δ = b2-4ac
Δ = 222-4·4·(-3)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{133}}{2*4}=\frac{-22-2\sqrt{133}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{133}}{2*4}=\frac{-22+2\sqrt{133}}{8}
$