14/2x=5x

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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} $

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