6/x+14=6/4x+5

Solution for 6/x+14=6/4x+5 equation:

6/x+14=6/4x+5

We move all terms to the left:

6/x+14-(6/4x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

6/x-6/4x-5+14=0

We calculate fractions


24x/4x^2+(-6x)/4x^2-5+14=0

We add all the numbers together, and all the variables

24x/4x^2+(-6x)/4x^2+9=0

We multiply all the terms by the denominator


24x+(-6x)+9*4x^2=0

Wy multiply elements

36x^2+24x+(-6x)=0

We get rid of parentheses

36x^2+24x-6x=0

We add all the numbers together, and all the variables

36x^2+18x=0

a = 36; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·36·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*36}=\frac{-36}{72}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*36}=\frac{0}{72}
=0
$