7(1/3)x=7/27

Solution for 7(1/3)x=7/27 equation:

7(1/3)x=7/27

We move all terms to the left:

7(1/3)x-(7/27)=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

7(+1/3)x-(+7/27)=0

We multiply parentheses

7x^2-(+7/27)=0

We get rid of parentheses

7x^2-7/27=0

We multiply all the terms by the denominator


7x^2*27-7=0

Wy multiply elements

189x^2-7=0

a = 189; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·189·(-7)
Δ = 5292
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:

$\sqrt{\Delta}=\sqrt{5292}=\sqrt{1764*3}=\sqrt{1764}*\sqrt{3}=42\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{3}}{2*189}=\frac{0-42\sqrt{3}}{378}
=-\frac{42\sqrt{3}}{378}
=-\frac{\sqrt{3}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{3}}{2*189}=\frac{0+42\sqrt{3}}{378}
=\frac{42\sqrt{3}}{378}
=\frac{\sqrt{3}}{9}
$