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2/3x+12x=18
We move all terms to the left:
2/3x+12x-(18)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
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} $
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