3z-5=2z^2

Solution for 3z-5=2z^2 equation:

Simplifying
3z + -5 = 2z2

Reorder the terms:
-5 + 3z = 2z2

Solving
-5 + 3z = 2z2

Solving for variable 'z'.

Combine like terms: 2z2 + -2z2 = 0
-5 + 3z + -2z2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
2.5 + -1.5z + z2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -1.5z + -2.5 + z2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -1.5z + z2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -1.5z + z2 = 0 + -2.5
-1.5z + z2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-1.5z + z2 = -2.5

The z term is -1.5z.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5z + 0.5625 + z2 = -2.5 + 0.5625

Reorder the terms:
0.5625 + -1.5z + z2 = -2.5 + 0.5625

Combine like terms: -2.5 + 0.5625 = -1.9375
0.5625 + -1.5z + z2 = -1.9375

Factor a perfect square on the left side:
(z + -0.75)(z + -0.75) = -1.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.