14/2x=5x

Solution for 14/2x=5x equation:

14/2x=5x

We move all terms to the left:

14/2x-(5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+14/2x=0

We multiply all the terms by the denominator


-5x*2x+14=0

Wy multiply elements

-10x^2+14=0

a = -10; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-10)·14
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*-10}=\frac{0-4\sqrt{35}}{-20}
=-\frac{4\sqrt{35}}{-20}
=-\frac{\sqrt{35}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*-10}=\frac{0+4\sqrt{35}}{-20}
=\frac{4\sqrt{35}}{-20}
=\frac{\sqrt{35}}{-5}
$