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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


(-1080x^2)/1296x^2+1728x^2/1296x^2+648x/1296x^2+(-216x)/1296x^2=0

We multiply all the terms by the denominator


(-1080x^2)+1728x^2+648x+(-216x)=0

We add all the numbers together, and all the variables

1728x^2+(-1080x^2)+648x+(-216x)=0

We get rid of parentheses

1728x^2-1080x^2+648x-216x=0

We add all the numbers together, and all the variables

648x^2+432x=0

a = 648; b = 432; c = 0;
Δ = b2-4ac
Δ = 4322-4·648·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(432)-432}{2*648}=\frac{-864}{1296}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(432)+432}{2*648}=\frac{0}{1296}
=0
$