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-4z^2-9z-4=0
a = -4; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·(-4)·(-4)
Δ = 17
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{17}}{2*-4}=\frac{9-\sqrt{17}}{-8} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{17}}{2*-4}=\frac{9+\sqrt{17}}{-8} $
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