(2/3)*x=9/2

Solution for (2/3)*x=9/2 equation:

(2/3)*x=9/2

We move all terms to the left:

(2/3)*x-(9/2)=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-(+9/2)=0

We multiply parentheses

2x^2-(+9/2)=0

We get rid of parentheses

2x^2-9/2=0

We multiply all the terms by the denominator


2x^2*2-9=0

Wy multiply elements

4x^2-9=0

a = 4; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·4·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*4}=\frac{12}{8}
=1+1/2
$