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9+5a=54/a=
We move all terms to the left:
9+5a-(54/a)=0
Domain of the equation: a)!=0We add all the numbers together, and all the variables
a!=0/1
a!=0
a∈R
5a-(+54/a)+9=0
We get rid of parentheses
5a-54/a+9=0
We multiply all the terms by the denominator
5a*a+9*a-54=0
We add all the numbers together, and all the variables
9a+5a*a-54=0
Wy multiply elements
5a^2+9a-54=0
a = 5; b = 9; c = -54;
Δ = b2-4ac
Δ = 92-4·5·(-54)
Δ = 1161
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{129}}{2*5}=\frac{-9-3\sqrt{129}}{10} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{129}}{2*5}=\frac{-9+3\sqrt{129}}{10} $
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