4x=2/7x

Solution for 4x=2/7x equation:

4x=2/7x

We move all terms to the left:

4x-(2/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+2/7x)=0

We get rid of parentheses

4x-2/7x=0

We multiply all the terms by the denominator


4x*7x-2=0

Wy multiply elements

28x^2-2=0

a = 28; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·28·(-2)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*28}=\frac{0-4\sqrt{14}}{56}
=-\frac{4\sqrt{14}}{56}
=-\frac{\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*28}=\frac{0+4\sqrt{14}}{56}
=\frac{4\sqrt{14}}{56}
=\frac{\sqrt{14}}{14}
$