(2/7)x=6/11

Solution for (2/7)x=6/11 equation:

(2/7)x=6/11

We move all terms to the left:

(2/7)x-(6/11)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/7)x-(+6/11)=0

We multiply parentheses

2x^2-(+6/11)=0

We get rid of parentheses

2x^2-6/11=0

We multiply all the terms by the denominator


2x^2*11-6=0

Wy multiply elements

22x^2-6=0

a = 22; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·22·(-6)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*22}=\frac{0-4\sqrt{33}}{44}
=-\frac{4\sqrt{33}}{44}
=-\frac{\sqrt{33}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*22}=\frac{0+4\sqrt{33}}{44}
=\frac{4\sqrt{33}}{44}
=\frac{\sqrt{33}}{11}
$