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10z^2+21z+9=0
a = 10; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·10·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-9}{2*10}=\frac{-30}{20} =-1+1/2 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9}{2*10}=\frac{-12}{20} =-3/5 $
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