45z^2+13=16z

Solution for 45z^2+13=16z equation:

Simplifying
45z2 + 13 = 16z

Reorder the terms:
13 + 45z2 = 16z

Solving
13 + 45z2 = 16z

Solving for variable 'z'.

Reorder the terms:
13 + -16z + 45z2 = 16z + -16z

Combine like terms: 16z + -16z = 0
13 + -16z + 45z2 = 0

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

Divide each side by '45'.
0.2888888889 + -0.3555555556z + z2 = 0

Move the constant term to the right:

Add '-0.2888888889' to each side of the equation.
0.2888888889 + -0.3555555556z + -0.2888888889 + z2 = 0 + -0.2888888889

Reorder the terms:
0.2888888889 + -0.2888888889 + -0.3555555556z + z2 = 0 + -0.2888888889

Combine like terms: 0.2888888889 + -0.2888888889 = 0.0000000000
0.0000000000 + -0.3555555556z + z2 = 0 + -0.2888888889
-0.3555555556z + z2 = 0 + -0.2888888889

Combine like terms: 0 + -0.2888888889 = -0.2888888889
-0.3555555556z + z2 = -0.2888888889

The z term is -0.3555555556z.  Take half its coefficient (-0.1777777778).
Square it (0.03160493828) and add it to both sides.

Add '0.03160493828' to each side of the equation.
-0.3555555556z + 0.03160493828 + z2 = -0.2888888889 + 0.03160493828

Reorder the terms:
0.03160493828 + -0.3555555556z + z2 = -0.2888888889 + 0.03160493828

Combine like terms: -0.2888888889 + 0.03160493828 = -0.25728395062
0.03160493828 + -0.3555555556z + z2 = -0.25728395062

Factor a perfect square on the left side:
(z + -0.1777777778)(z + -0.1777777778) = -0.25728395062

Can't calculate square root of the right side.

The solution to this equation could not be determined.