6/x+14=4/3x

Solution for 6/x+14=4/3x equation:

6/x+14=4/3x

We move all terms to the left:

6/x+14-(4/3x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6/x-(+4/3x)+14=0

We get rid of parentheses

6/x-4/3x+14=0

We calculate fractions


18x/3x^2+(-4x)/3x^2+14=0

We multiply all the terms by the denominator


18x+(-4x)+14*3x^2=0

Wy multiply elements

42x^2+18x+(-4x)=0

We get rid of parentheses

42x^2+18x-4x=0

We add all the numbers together, and all the variables

42x^2+14x=0

a = 42; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·42·0
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*42}=\frac{-28}{84}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*42}=\frac{0}{84}
=0
$