14/15x=x

Solution for 14/15x=x equation:

14/15x=x

We move all terms to the left:

14/15x-(x)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+14/15x=0

We multiply all the terms by the denominator


-1x*15x+14=0

Wy multiply elements

-15x^2+14=0

a = -15; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-15)·14
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*-15}=\frac{0-2\sqrt{210}}{-30}
=-\frac{2\sqrt{210}}{-30}
=-\frac{\sqrt{210}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*-15}=\frac{0+2\sqrt{210}}{-30}
=\frac{2\sqrt{210}}{-30}
=\frac{\sqrt{210}}{-15}
$