1/6x+x+2x=90

Solution for 1/6x+x+2x=90 equation:

1/6x+x+2x=90

We move all terms to the left:

1/6x+x+2x-(90)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/6x-90=0

We multiply all the terms by the denominator


3x*6x-90*6x+1=0

Wy multiply elements

18x^2-540x+1=0

a = 18; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·18·1
Δ = 291528
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:

$\sqrt{\Delta}=\sqrt{291528}=\sqrt{36*8098}=\sqrt{36}*\sqrt{8098}=6\sqrt{8098}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-6\sqrt{8098}}{2*18}=\frac{540-6\sqrt{8098}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+6\sqrt{8098}}{2*18}=\frac{540+6\sqrt{8098}}{36}
$