2/3x-2/7-5/6x=12

Solution for 2/3x-2/7-5/6x=12 equation:

2/3x-2/7-5/6x=12

We move all terms to the left:

2/3x-2/7-5/6x-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


determiningTheFunctionDomain
2/3x-5/6x-12-2/7=0

We calculate fractions


(-216x^2)/882x^2+588x/882x^2+(-735x)/882x^2-12=0

We multiply all the terms by the denominator


(-216x^2)+588x+(-735x)-12*882x^2=0

Wy multiply elements

(-216x^2)-10584x^2+588x+(-735x)=0

We get rid of parentheses

-216x^2-10584x^2+588x-735x=0

We add all the numbers together, and all the variables

-10800x^2-147x=0

a = -10800; b = -147; c = 0;
Δ = b2-4ac
Δ = -1472-4·(-10800)·0
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-147)-147}{2*-10800}=\frac{0}{-21600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+147}{2*-10800}=\frac{294}{-21600}
=-49/3600
$