35/7x=x

Solution for 35/7x=x equation:

35/7x=x

We move all terms to the left:

35/7x-(x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+35/7x=0

We multiply all the terms by the denominator


-1x*7x+35=0

Wy multiply elements

-7x^2+35=0

a = -7; b = 0; c = +35;
Δ = b2-4ac
Δ = 02-4·(-7)·35
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{5}}{2*-7}=\frac{0-14\sqrt{5}}{-14}
=-\frac{14\sqrt{5}}{-14}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{5}}{2*-7}=\frac{0+14\sqrt{5}}{-14}
=\frac{14\sqrt{5}}{-14}
=\frac{\sqrt{5}}{-1}
$