1/3x+6/x=10

Solution for 1/3x+6/x=10 equation:

1/3x+6/x=10

We move all terms to the left:

1/3x+6/x-(10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


x/3x^2+18x/3x^2-10=0

We multiply all the terms by the denominator


x+18x-10*3x^2=0

We add all the numbers together, and all the variables

19x-10*3x^2=0

Wy multiply elements

-30x^2+19x=0

a = -30; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-30)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-30}=\frac{-38}{-60}
=19/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-30}=\frac{0}{-60}
=0
$