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: 3*6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


x*3*6x+5*3*6x-1=0

Wy multiply elements

18x^2*6+90x*6-1=0

Wy multiply elements

108x^2+540x-1=0

a = 108; b = 540; c = -1;
Δ = b2-4ac
Δ = 5402-4·108·(-1)
Δ = 292032
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:

$\sqrt{\Delta}=\sqrt{292032}=\sqrt{97344*3}=\sqrt{97344}*\sqrt{3}=312\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-312\sqrt{3}}{2*108}=\frac{-540-312\sqrt{3}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+312\sqrt{3}}{2*108}=\frac{-540+312\sqrt{3}}{216}
$