3x^-1=3/2x

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

3x^-1=3/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x^-(+3/2x)-1=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-3/2x-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-2x-3=0

a = 6; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·6·(-3)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*6}=\frac{2-2\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*6}=\frac{2+2\sqrt{19}}{12}
$