(16/9)x-(2/3)=2/3

Solution for (16/9)x-(2/3)=2/3 equation:

(16/9)x-(2/3)=2/3

We move all terms to the left:

(16/9)x-(2/3)-(2/3)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+16/9)x-(+2/3)-(+2/3)=0

We multiply parentheses

16x^2-(+2/3)-(+2/3)=0

We get rid of parentheses

16x^2-2/3-2/3=0

We multiply all the terms by the denominator


16x^2*3-2-2=0

We add all the numbers together, and all the variables

16x^2*3-4=0

Wy multiply elements

48x^2-4=0

a = 48; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·48·(-4)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*48}=\frac{0-16\sqrt{3}}{96}
=-\frac{16\sqrt{3}}{96}
=-\frac{\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*48}=\frac{0+16\sqrt{3}}{96}
=\frac{16\sqrt{3}}{96}
=\frac{\sqrt{3}}{6}
$