-11/6x-1/7x=-83/56

Solution for -11/6x-1/7x=-83/56 equation:

-11/6x-1/7x=-83/56

We move all terms to the left:

-11/6x-1/7x-(-83/56)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

-11/6x-1/7x+83/56=0

We calculate fractions


24402x^2/11760x^2+(-21560x)/11760x^2+(-1680x)/11760x^2=0

We multiply all the terms by the denominator


24402x^2+(-21560x)+(-1680x)=0

We get rid of parentheses

24402x^2-21560x-1680x=0

We add all the numbers together, and all the variables

24402x^2-23240x=0

a = 24402; b = -23240; c = 0;
Δ = b2-4ac
Δ = -232402-4·24402·0
Δ = 540097600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{540097600}=23240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23240)-23240}{2*24402}=\frac{0}{48804}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23240)+23240}{2*24402}=\frac{46480}{48804}
=20/21
$