2z^2-(5-i)z+6=0

Solution for 2z^2-(5-i)z+6=0 equation:

Simplifying
2z2 + -1(5 + -1i) * z + 6 = 0

Reorder the terms for easier multiplication:
2z2 + -1z(5 + -1i) + 6 = 0
2z2 + (5 * -1z + -1i * -1z) + 6 = 0

Reorder the terms:
2z2 + (1iz + -5z) + 6 = 0
2z2 + (1iz + -5z) + 6 = 0

Reorder the terms:
6 + 1iz + -5z + 2z2 = 0

Solving
6 + 1iz + -5z + 2z2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + 1iz + -5z + -6 + 2z2 = 0 + -6

Reorder the terms:
6 + -6 + 1iz + -5z + 2z2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 1iz + -5z + 2z2 = 0 + -6
1iz + -5z + 2z2 = 0 + -6

Combine like terms: 0 + -6 = -6
1iz + -5z + 2z2 = -6

Add '5z' to each side of the equation.
1iz + -5z + 5z + 2z2 = -6 + 5z

Combine like terms: -5z + 5z = 0
1iz + 0 + 2z2 = -6 + 5z
1iz + 2z2 = -6 + 5z

Add '-2z2' to each side of the equation.
1iz + 2z2 + -2z2 = -6 + 5z + -2z2

Combine like terms: 2z2 + -2z2 = 0
1iz + 0 = -6 + 5z + -2z2
1iz = -6 + 5z + -2z2

Divide each side by '1z'.
i = -6z-1 + 5 + -2z

Simplifying
i = -6z-1 + 5 + -2z

Reorder the terms:
i = 5 + -6z-1 + -2z