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3a=1/3a+15
We move all terms to the left:
3a-(1/3a+15)=0
Domain of the equation: 3a+15)!=0We get rid of parentheses
a∈R
3a-1/3a-15=0
We multiply all the terms by the denominator
3a*3a-15*3a-1=0
Wy multiply elements
9a^2-45a-1=0
a = 9; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·9·(-1)
Δ = 2061
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2061}=\sqrt{9*229}=\sqrt{9}*\sqrt{229}=3\sqrt{229}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{229}}{2*9}=\frac{45-3\sqrt{229}}{18} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{229}}{2*9}=\frac{45+3\sqrt{229}}{18} $
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