(6/2x)+(4/x)=14

Solution for (6/2x)+(4/x)=14 equation:

(6/2x)+(4/x)=14

We move all terms to the left:

(6/2x)+(4/x)-(14)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+6/2x)+(+4/x)-14=0

We get rid of parentheses

6/2x+4/x-14=0

We calculate fractions


6x/2x^2+8x/2x^2-14=0

We multiply all the terms by the denominator


6x+8x-14*2x^2=0

We add all the numbers together, and all the variables

14x-14*2x^2=0

Wy multiply elements

-28x^2+14x=0

a = -28; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-28)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-28}=\frac{-28}{-56}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-28}=\frac{0}{-56}
=0
$