6/x=2/3x+10

Solution for 6/x=2/3x+10 equation:

6/x=2/3x+10

We move all terms to the left:

6/x-(2/3x+10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

6/x-2/3x-10=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-30x^2+18x+(-2x)=0

We get rid of parentheses

-30x^2+18x-2x=0

We add all the numbers together, and all the variables

-30x^2+16x=0

a = -30; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-30)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-30}=\frac{-32}{-60}
=8/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-30}=\frac{0}{-60}
=0
$