x+5=1/3(6x)

Solution for x+5=1/3(6x) equation:

x+5=1/3(6x)

We move all terms to the left:

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


Domain of the equation: 36x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/36x)+5=0

We get rid of parentheses

x-1/36x+5=0

We multiply all the terms by the denominator


x*36x+5*36x-1=0

Wy multiply elements

36x^2+180x-1=0

a = 36; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·36·(-1)
Δ = 32544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32544}=\sqrt{144*226}=\sqrt{144}*\sqrt{226}=12\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{226}}{2*36}=\frac{-180-12\sqrt{226}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{226}}{2*36}=\frac{-180+12\sqrt{226}}{72}
$