10/x=6/3x+5

Solution for 10/x=6/3x+5 equation:

10/x=6/3x+5

We move all terms to the left:

10/x-(6/3x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

10/x-6/3x-5=0

We calculate fractions


30x/3x^2+(-6x)/3x^2-5=0

We multiply all the terms by the denominator


30x+(-6x)-5*3x^2=0

Wy multiply elements

-15x^2+30x+(-6x)=0

We get rid of parentheses

-15x^2+30x-6x=0

We add all the numbers together, and all the variables

-15x^2+24x=0

a = -15; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-15)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-15}=\frac{-48}{-30}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-15}=\frac{0}{-30}
=0
$