6/x=6/5x+1

Solution for 6/x=6/5x+1 equation:

6/x=6/5x+1

We move all terms to the left:

6/x-(6/5x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

6/x-6/5x-1=0

We calculate fractions


30x/5x^2+(-6x)/5x^2-1=0

We multiply all the terms by the denominator


30x+(-6x)-1*5x^2=0

Wy multiply elements

-5x^2+30x+(-6x)=0

We get rid of parentheses

-5x^2+30x-6x=0

We add all the numbers together, and all the variables

-5x^2+24x=0

a = -5; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-5)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-5}=\frac{-48}{-10}
=4+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-5}=\frac{0}{-10}
=0
$