-11/6x-2/3x=83/14

Solution for -11/6x-2/3x=83/14 equation:

-11/6x-2/3x=83/14

We move all terms to the left:

-11/6x-2/3x-(83/14)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-11/6x-2/3x-(+83/14)=0

We get rid of parentheses

-11/6x-2/3x-83/14=0

We calculate fractions


(-4482x^2)/252x^2+(-462x)/252x^2+(-168x)/252x^2=0

We multiply all the terms by the denominator


(-4482x^2)+(-462x)+(-168x)=0

We get rid of parentheses

-4482x^2-462x-168x=0

We add all the numbers together, and all the variables

-4482x^2-630x=0

a = -4482; b = -630; c = 0;
Δ = b2-4ac
Δ = -6302-4·(-4482)·0
Δ = 396900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{396900}=630$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-630}{2*-4482}=\frac{0}{-8964}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+630}{2*-4482}=\frac{1260}{-8964}
=-35/249
$