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1/2x+1/3x=1/18
We move all terms to the left:
1/2x+1/3x-(1/18)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
1/2x+1/3x-(+1/18)=0
We get rid of parentheses
1/2x+1/3x-1/18=0
We calculate fractions
(-18x^2)/108x^2+54x/108x^2+36x/108x^2=0
We multiply all the terms by the denominator
(-18x^2)+54x+36x=0
We add all the numbers together, and all the variables
(-18x^2)+90x=0
We get rid of parentheses
-18x^2+90x=0
a = -18; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-18)·0
Δ = 8100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{8100}=90$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-18}=\frac{-180}{-36} =+5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-18}=\frac{0}{-36} =0 $
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