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3a+(2a+6)a=2
We move all terms to the left:
3a+(2a+6)a-(2)=0
We multiply parentheses
2a^2+3a+6a-2=0
We add all the numbers together, and all the variables
2a^2+9a-2=0
a = 2; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·2·(-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{-(9)-\sqrt{97}}{2*2}=\frac{-9-\sqrt{97}}{4} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{97}}{2*2}=\frac{-9+\sqrt{97}}{4} $
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