5/x=12/2x-14

Solution for 5/x=12/2x-14 equation:

5/x=12/2x-14

We move all terms to the left:

5/x-(12/2x-14)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-14)!=0

x∈R


We get rid of parentheses

5/x-12/2x+14=0

We calculate fractions


10x/2x^2+(-12x)/2x^2+14=0

We multiply all the terms by the denominator


10x+(-12x)+14*2x^2=0

Wy multiply elements

28x^2+10x+(-12x)=0

We get rid of parentheses

28x^2+10x-12x=0

We add all the numbers together, and all the variables

28x^2-2x=0

a = 28; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·28·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*28}=\frac{0}{56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*28}=\frac{4}{56}
=1/14
$