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z^2+20.5z=144
We move all terms to the left:
z^2+20.5z-(144)=0
a = 1; b = 20.5; c = -144;
Δ = b2-4ac
Δ = 20.52-4·1·(-144)
Δ = 996.25
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{-(20.5)-\sqrt{996.25}}{2*1}=\frac{-20.5-\sqrt{996.25}}{2} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20.5)+\sqrt{996.25}}{2*1}=\frac{-20.5+\sqrt{996.25}}{2} $
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