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18=x+2/3x
We move all terms to the left:
18-(x+2/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-(+x+2/3x)+18=0
We get rid of parentheses
-x-2/3x+18=0
We multiply all the terms by the denominator
-x*3x+18*3x-2=0
Wy multiply elements
-3x^2+54x-2=0
a = -3; b = 54; c = -2;
Δ = b2-4ac
Δ = 542-4·(-3)·(-2)
Δ = 2892
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{723}}{2*-3}=\frac{-54-2\sqrt{723}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{723}}{2*-3}=\frac{-54+2\sqrt{723}}{-6} $
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