x-1/6x+11=x-1/5x+3

Solution for x-1/6x+11=x-1/5x+3 equation:

x-1/6x+11=x-1/5x+3

We move all terms to the left:

x-1/6x+11-(x-1/5x+3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x+3)!=0

x∈R


We get rid of parentheses

x-1/6x-x+1/5x-3+11=0

We calculate fractions


x-x+(-5x)/30x^2+6x/30x^2-3+11=0

We add all the numbers together, and all the variables

(-5x)/30x^2+6x/30x^2+8=0

We multiply all the terms by the denominator


(-5x)+6x+8*30x^2=0

We add all the numbers together, and all the variables

6x+(-5x)+8*30x^2=0

Wy multiply elements

240x^2+6x+(-5x)=0

We get rid of parentheses

240x^2+6x-5x=0

We add all the numbers together, and all the variables

240x^2+x=0

a = 240; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·240·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*240}=\frac{-2}{480}
=-1/240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*240}=\frac{0}{480}
=0
$