1/x+2/3-1/6x=5/12

Solution for 1/x+2/3-1/6x=5/12 equation:

1/x+2/3-1/6x=5/12

We move all terms to the left:

1/x+2/3-1/6x-(5/12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/x-1/6x+2/3-(+5/12)=0

We get rid of parentheses

1/x-1/6x+2/3-5/12=0

We calculate fractions


(-540x^2)/648x^2+864x^2/648x^2+648x/648x^2+(-108x)/648x^2=0

We multiply all the terms by the denominator


(-540x^2)+864x^2+648x+(-108x)=0

We add all the numbers together, and all the variables

864x^2+(-540x^2)+648x+(-108x)=0

We get rid of parentheses

864x^2-540x^2+648x-108x=0

We add all the numbers together, and all the variables

324x^2+540x=0

a = 324; b = 540; c = 0;
Δ = b2-4ac
Δ = 5402-4·324·0
Δ = 291600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{291600}=540$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-540}{2*324}=\frac{-1080}{648}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+540}{2*324}=\frac{0}{648}
=0
$