Given: z – = 4z + 5
On multiplying both sides by z, we get:
z2 – 7 = 4z2 + 5z
On transposing all the terms of the right-hand side to the left-hand side, we get:
z2 – 7 – 4z2 – 5z = 0
– 3z2 – 5z – 7 = 0
On comparing this equation with the general form of the quadratic equation az2 + bz + c = 0, we get:
a = –3, b = –5 and c = –7, which are real numbers and a 0.
Thus, the given equation is a quadratic equation in the variable z.