15-1/5x=1/6x-1

Solution for 15-1/5x=1/6x-1 equation:

15-1/5x=1/6x-1

We move all terms to the left:

15-1/5x-(1/6x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x-1)!=0

x∈R


We get rid of parentheses

-1/5x-1/6x+1+15=0

We calculate fractions


(-6x)/30x^2+(-5x)/30x^2+1+15=0

We add all the numbers together, and all the variables

(-6x)/30x^2+(-5x)/30x^2+16=0

We multiply all the terms by the denominator


(-6x)+(-5x)+16*30x^2=0

Wy multiply elements

480x^2+(-6x)+(-5x)=0

We get rid of parentheses

480x^2-6x-5x=0

We add all the numbers together, and all the variables

480x^2-11x=0

a = 480; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·480·0
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*480}=\frac{0}{960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*480}=\frac{22}{960}
=11/480
$