1/6x-1/5x=8

Solution for 1/6x-1/5x=8 equation:

1/6x-1/5x=8

We move all terms to the left:

1/6x-1/5x-(8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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