1/5x-1/6x+1/30=5

Solution for 1/5x-1/6x+1/30=5 equation:

1/5x-1/6x+1/30=5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


determiningTheFunctionDomain
1/5x-1/6x-5+1/30=0

We calculate fractions


180x^2/2700x^2+540x/2700x^2+(-450x)/2700x^2-5=0

We multiply all the terms by the denominator


180x^2+540x+(-450x)-5*2700x^2=0

Wy multiply elements

180x^2-13500x^2+540x+(-450x)=0

We get rid of parentheses

180x^2-13500x^2+540x-450x=0

We add all the numbers together, and all the variables

-13320x^2+90x=0

a = -13320; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-13320)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-13320}=\frac{-180}{-26640}
=1/148
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-13320}=\frac{0}{-26640}
=0
$