1.5x-2=3/2x

Solution for 1.5x-2=3/2x equation:

1.5x-2=3/2x

We move all terms to the left:

1.5x-2-(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

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

We get rid of parentheses

1.5x-3/2x-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-2*2x-3=0

Wy multiply elements

2x^2-4x-3=0

a = 2; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·2·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*2}=\frac{4-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*2}=\frac{4+2\sqrt{10}}{4}
$