1/x+1/5x=6

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

1/x+1/5x=6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-6*5x^2=0

Wy multiply elements

-30x^2+6x=0

a = -30; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-30)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-30}=\frac{-12}{-60}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-30}=\frac{0}{-60}
=0
$