X+1/3x+x-30=180

Solution for X+1/3x+x-30=180 equation:

X+1/3X+X-30=180

We move all terms to the left:

X+1/3X+X-30-(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

2X+1/3X-210=0

We multiply all the terms by the denominator


2X*3X-210*3X+1=0

Wy multiply elements

6X^2-630X+1=0

a = 6; b = -630; c = +1;
Δ = b2-4ac
Δ = -6302-4·6·1
Δ = 396876
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:

$\sqrt{\Delta}=\sqrt{396876}=\sqrt{4*99219}=\sqrt{4}*\sqrt{99219}=2\sqrt{99219}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99219}}{2*6}=\frac{630-2\sqrt{99219}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99219}}{2*6}=\frac{630+2\sqrt{99219}}{12}
$