X-24+1/3x+12+2x-108=180

Solution for X-24+1/3x+12+2x-108=180 equation:

X-24+1/3X+12+2X-108=180

We move all terms to the left:

X-24+1/3X+12+2X-108-(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

3X+1/3X-300=0

We multiply all the terms by the denominator


3X*3X-300*3X+1=0

Wy multiply elements

9X^2-900X+1=0

a = 9; b = -900; c = +1;
Δ = b2-4ac
Δ = -9002-4·9·1
Δ = 809964
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:

$\sqrt{\Delta}=\sqrt{809964}=\sqrt{36*22499}=\sqrt{36}*\sqrt{22499}=6\sqrt{22499}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-6\sqrt{22499}}{2*9}=\frac{900-6\sqrt{22499}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+6\sqrt{22499}}{2*9}=\frac{900+6\sqrt{22499}}{18}
$