solve by completing the squares.
5z^2+19z-4=0
5z^2+19z-4=0
divide each term by 5
z^2 + (19/5)z + .... = 4/5 + ....
take 1/2 of the 19/5, square it, and add it to both sides
z^2 + (19/5)z + 361/100 = 4/5 + 361/100
(z + 19/10)^2 = 441/100
take √ of both sides
z + 19/10 = ± 21/10
z = ±21/10 - 19/10 = .....