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1/a+1/3a+8=22
We move all terms to the left:
1/a+1/3a+8-(22)=0
Domain of the equation: a!=0
a∈R
Domain of the equation: 3a!=0We add all the numbers together, and all the variables
a!=0/3
a!=0
a∈R
1/a+1/3a-14=0
We calculate fractions
3a/3a^2+a/3a^2-14=0
We multiply all the terms by the denominator
3a+a-14*3a^2=0
We add all the numbers together, and all the variables
4a-14*3a^2=0
Wy multiply elements
-42a^2+4a=0
a = -42; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-42)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{16}=4$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-42}=\frac{-8}{-84} =2/21 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-42}=\frac{0}{-84} =0 $
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