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9q^2-12q-21=0
a = 9; b = -12; c = -21;
Δ = b2-4ac
Δ = -122-4·9·(-21)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{900}=30$$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-30}{2*9}=\frac{-18}{18} =-1 $$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+30}{2*9}=\frac{42}{18} =2+1/3 $
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