-13/6x+13/3x=13/8

Solution for -13/6x+13/3x=13/8 equation:

-13/6x+13/3x=13/8

We move all terms to the left:

-13/6x+13/3x-(13/8)=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

-13/6x+13/3x-(+13/8)=0

We get rid of parentheses

-13/6x+13/3x-13/8=0

We calculate fractions


(-702x^2)/1152x^2+(-2496x)/1152x^2+4992x/1152x^2=0

We multiply all the terms by the denominator


(-702x^2)+(-2496x)+4992x=0

We add all the numbers together, and all the variables

(-702x^2)+4992x+(-2496x)=0

We get rid of parentheses

-702x^2+4992x-2496x=0

We add all the numbers together, and all the variables

-702x^2+2496x=0

a = -702; b = 2496; c = 0;
Δ = b2-4ac
Δ = 24962-4·(-702)·0
Δ = 6230016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6230016}=2496$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2496)-2496}{2*-702}=\frac{-4992}{-1404}
=3+5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2496)+2496}{2*-702}=\frac{0}{-1404}
=0
$