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3a+2/a=11
We move all terms to the left:
3a+2/a-(11)=0
Domain of the equation: a!=0We multiply all the terms by the denominator
a∈R
3a*a-11*a+2=0
We add all the numbers together, and all the variables
-11a+3a*a+2=0
Wy multiply elements
3a^2-11a+2=0
a = 3; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·3·2
Δ = 97
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{97}}{2*3}=\frac{11-\sqrt{97}}{6} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*3}=\frac{11+\sqrt{97}}{6} $
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