(3/2)x=4/9

Solution for (3/2)x=4/9 equation:

(3/2)x=4/9

We move all terms to the left:

(3/2)x-(4/9)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/2)x-(+4/9)=0

We multiply parentheses

3x^2-(+4/9)=0

We get rid of parentheses

3x^2-4/9=0

We multiply all the terms by the denominator


3x^2*9-4=0

Wy multiply elements

27x^2-4=0

a = 27; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·27·(-4)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*27}=\frac{0-12\sqrt{3}}{54}
=-\frac{12\sqrt{3}}{54}
=-\frac{2\sqrt{3}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*27}=\frac{0+12\sqrt{3}}{54}
=\frac{12\sqrt{3}}{54}
=\frac{2\sqrt{3}}{9}
$