(2/3)*x=3/2

Solution for (2/3)*x=3/2 equation:

(2/3)*x=3/2

We move all terms to the left:

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


Domain of the equation: 3)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

2x^2-3/2=0

We multiply all the terms by the denominator


2x^2*2-3=0

Wy multiply elements

4x^2-3=0

a = 4; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·4·(-3)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*4}=\frac{0-4\sqrt{3}}{8}
=-\frac{4\sqrt{3}}{8}
=-\frac{\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*4}=\frac{0+4\sqrt{3}}{8}
=\frac{4\sqrt{3}}{8}
=\frac{\sqrt{3}}{2}
$