7/5x=x

Solution for 7/5x=x equation:

7/5x=x

We move all terms to the left:

7/5x-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/5x=0

We multiply all the terms by the denominator


-1x*5x+7=0

Wy multiply elements

-5x^2+7=0

a = -5; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-5)·7
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*-5}=\frac{0-2\sqrt{35}}{-10}
=-\frac{2\sqrt{35}}{-10}
=-\frac{\sqrt{35}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*-5}=\frac{0+2\sqrt{35}}{-10}
=\frac{2\sqrt{35}}{-10}
=\frac{\sqrt{35}}{-5}
$