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1/2x+8=1/9x
We move all terms to the left:
1/2x+8-(1/9x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 9x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/2x-(+1/9x)+8=0
We get rid of parentheses
1/2x-1/9x+8=0
We calculate fractions
9x/18x^2+(-2x)/18x^2+8=0
We multiply all the terms by the denominator
9x+(-2x)+8*18x^2=0
Wy multiply elements
144x^2+9x+(-2x)=0
We get rid of parentheses
144x^2+9x-2x=0
We add all the numbers together, and all the variables
144x^2+7x=0
a = 144; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·144·0
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*144}=\frac{-14}{288} =-7/144 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*144}=\frac{0}{288} =0 $
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