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3a+1/2a=9
We move all terms to the left:
3a+1/2a-(9)=0
Domain of the equation: 2a!=0We multiply all the terms by the denominator
a!=0/2
a!=0
a∈R
3a*2a-9*2a+1=0
Wy multiply elements
6a^2-18a+1=0
a = 6; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·6·1
Δ = 300
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*6}=\frac{18-10\sqrt{3}}{12} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*6}=\frac{18+10\sqrt{3}}{12} $
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