10/x=11/3x+6.

Solution for 10/x=11/3x+6. equation:

10/x=11/3x+6.

We move all terms to the left:

10/x-(11/3x+6.)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+6.)!=0

x∈R


We add all the numbers together, and all the variables

10/x-(11/3x+6)=0

We get rid of parentheses

10/x-11/3x-6=0

We calculate fractions


30x/3x^2+(-11x)/3x^2-6=0

We multiply all the terms by the denominator


30x+(-11x)-6*3x^2=0

Wy multiply elements

-18x^2+30x+(-11x)=0

We get rid of parentheses

-18x^2+30x-11x=0

We add all the numbers together, and all the variables

-18x^2+19x=0

a = -18; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-18)·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*-18}=\frac{-38}{-36}
=1+1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-18}=\frac{0}{-36}
=0
$