6/7x-1/3x=11

Solution for 6/7x-1/3x=11 equation:

6/7x-1/3x=11

We move all terms to the left:

6/7x-1/3x-(11)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


18x/21x^2+(-7x)/21x^2-11=0

We multiply all the terms by the denominator


18x+(-7x)-11*21x^2=0

Wy multiply elements

-231x^2+18x+(-7x)=0

We get rid of parentheses

-231x^2+18x-7x=0

We add all the numbers together, and all the variables

-231x^2+11x=0

a = -231; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-231)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-231}=\frac{-22}{-462}
=1/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-231}=\frac{0}{-462}
=0
$