x+6x-1/3x=180

Solution for x+6x-1/3x=180 equation:

x+6x-1/3x=180

We move all terms to the left:

x+6x-1/3x-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7x-1/3x-180=0

We multiply all the terms by the denominator


7x*3x-180*3x-1=0

Wy multiply elements

21x^2-540x-1=0

a = 21; b = -540; c = -1;
Δ = b2-4ac
Δ = -5402-4·21·(-1)
Δ = 291684
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:

$\sqrt{\Delta}=\sqrt{291684}=\sqrt{4*72921}=\sqrt{4}*\sqrt{72921}=2\sqrt{72921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72921}}{2*21}=\frac{540-2\sqrt{72921}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72921}}{2*21}=\frac{540+2\sqrt{72921}}{42}
$