3/2x-6=2x-1

Solution for 3/2x-6=2x-1 equation:

3/2x-6=2x-1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-2x+1-6=0

We multiply all the terms by the denominator


-2x*2x+1*2x-6*2x+3=0

Wy multiply elements

-4x^2+2x-12x+3=0

We add all the numbers together, and all the variables

-4x^2-10x+3=0

a = -4; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·(-4)·3
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*-4}=\frac{10-2\sqrt{37}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*-4}=\frac{10+2\sqrt{37}}{-8}
$