10-1/3x=3/x+5

Solution for 10-1/3x=3/x+5 equation:

10-1/3x=3/x+5

We move all terms to the left:

10-1/3x-(3/x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

-1/3x-3/x-5+10=0

We calculate fractions


(-x)/3x^2+(-9x)/3x^2-5+10=0

We add all the numbers together, and all the variables

(-1x)/3x^2+(-9x)/3x^2-5+10=0

We add all the numbers together, and all the variables

(-1x)/3x^2+(-9x)/3x^2+5=0

We multiply all the terms by the denominator


(-1x)+(-9x)+5*3x^2=0

Wy multiply elements

15x^2+(-1x)+(-9x)=0

We get rid of parentheses

15x^2-1x-9x=0

We add all the numbers together, and all the variables

15x^2-10x=0

a = 15; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·15·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*15}=\frac{20}{30}
=2/3
$