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8/3a+8=-2/a-1
We move all terms to the left:
8/3a+8-(-2/a-1)=0
Domain of the equation: 3a!=0
a!=0/3
a!=0
a∈R
Domain of the equation: a-1)!=0We get rid of parentheses
a∈R
8/3a+2/a+1+8=0
We calculate fractions
8a/3a^2+6a/3a^2+1+8=0
We add all the numbers together, and all the variables
8a/3a^2+6a/3a^2+9=0
We multiply all the terms by the denominator
8a+6a+9*3a^2=0
We add all the numbers together, and all the variables
14a+9*3a^2=0
Wy multiply elements
27a^2+14a=0
a = 27; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·27·0
Δ = 196
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{196}=14$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*27}=\frac{-28}{54} =-14/27 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*27}=\frac{0}{54} =0 $
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