1/3x+8/x=10

Solution for 1/3x+8/x=10 equation:

1/3x+8/x=10

We move all terms to the left:

1/3x+8/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+24x/3x^2-10=0

We multiply all the terms by the denominator


x+24x-10*3x^2=0

We add all the numbers together, and all the variables

25x-10*3x^2=0

Wy multiply elements

-30x^2+25x=0

a = -30; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-30)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-30}=\frac{-50}{-60}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-30}=\frac{0}{-60}
=0
$