2x=10/7x

Solution for 2x=10/7x equation:

2x=10/7x

We move all terms to the left:

2x-(10/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+10/7x)=0

We get rid of parentheses

2x-10/7x=0

We multiply all the terms by the denominator


2x*7x-10=0

Wy multiply elements

14x^2-10=0

a = 14; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·14·(-10)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{35}}{2*14}=\frac{0-4\sqrt{35}}{28}
=-\frac{4\sqrt{35}}{28}
=-\frac{\sqrt{35}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*14}=\frac{0+4\sqrt{35}}{28}
=\frac{4\sqrt{35}}{28}
=\frac{\sqrt{35}}{7}
$