14x=50/x

Solution for 14x=50/x equation:

14x=50/x

We move all terms to the left:

14x-(50/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

14x-(+50/x)=0

We get rid of parentheses

14x-50/x=0

We multiply all the terms by the denominator


14x*x-50=0

Wy multiply elements

14x^2-50=0

a = 14; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·14·(-50)
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{7}}{2*14}=\frac{0-20\sqrt{7}}{28}
=-\frac{20\sqrt{7}}{28}
=-\frac{5\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{7}}{2*14}=\frac{0+20\sqrt{7}}{28}
=\frac{20\sqrt{7}}{28}
=\frac{5\sqrt{7}}{7}
$