2/3x+12x=18

Solution for 2/3x+12x=18 equation:

2/3x+12x=18

We move all terms to the left:

2/3x+12x-(18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

12x+2/3x-18=0

We multiply all the terms by the denominator


12x*3x-18*3x+2=0

Wy multiply elements

36x^2-54x+2=0

a = 36; b = -54; c = +2;
Δ = b2-4ac
Δ = -542-4·36·2
Δ = 2628
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:

$\sqrt{\Delta}=\sqrt{2628}=\sqrt{36*73}=\sqrt{36}*\sqrt{73}=6\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{73}}{2*36}=\frac{54-6\sqrt{73}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{73}}{2*36}=\frac{54+6\sqrt{73}}{72}
$