8(1/6x)+x+1/6x=15/3

Solution for 8(1/6x)+x+1/6x=15/3 equation:

8(1/6x)+x+1/6x=15/3

We move all terms to the left:

8(1/6x)+x+1/6x-(15/3)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x+8x+1/6x-5=0

We multiply all the terms by the denominator


x*6x+8x*6x-5*6x+1=0

Wy multiply elements

6x^2+48x^2-30x+1=0

We add all the numbers together, and all the variables

54x^2-30x+1=0

a = 54; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·54·1
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{19}}{2*54}=\frac{30-6\sqrt{19}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{19}}{2*54}=\frac{30+6\sqrt{19}}{108}
$