3x/x+x/6=11/2

Solution for 3x/x+x/6=11/2 equation:

3x/x+x/6=11/2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x/x+x/6-11/2=0

We calculate fractions


4x^2/24x+72x/24x+(-396x)/24x=0

We multiply all the terms by the denominator


4x^2+72x+(-396x)=0

We get rid of parentheses

4x^2+72x-396x=0

We add all the numbers together, and all the variables

4x^2-324x=0

a = 4; b = -324; c = 0;
Δ = b2-4ac
Δ = -3242-4·4·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-324}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+324}{2*4}=\frac{648}{8}
=81
$