3/2x=1.5x

Solution for 3/2x=1.5x equation:

3/2x=1.5x

We move all terms to the left:

3/2x-(1.5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(+1.5x)=0

We get rid of parentheses

3/2x-1.5x=0

We multiply all the terms by the denominator


-(1.5x)*2x+3=0

We add all the numbers together, and all the variables

-(+1.5x)*2x+3=0

We multiply parentheses

-2x^2+3=0

a = -2; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-2)·3
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-2}=\frac{0-2\sqrt{6}}{-4}
=-\frac{2\sqrt{6}}{-4}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-2}=\frac{0+2\sqrt{6}}{-4}
=\frac{2\sqrt{6}}{-4}
=\frac{\sqrt{6}}{-2}
$