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

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

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

We move all terms to the left:

1/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

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2-1x=0

a = -5; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-5)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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