3z^2-5z+3=0

Solution for 3z^2-5z+3=0 equation:

Simplifying
3z2 + -5z + 3 = 0

Reorder the terms:
3 + -5z + 3z2 = 0

Solving
3 + -5z + 3z2 = 0

Solving for variable 'z'.

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

Divide each side by '3'.
1 + -1.666666667z + z2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.666666667z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + -1.666666667z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.666666667z + z2 = 0 + -1
-1.666666667z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.666666667z + z2 = -1

The z term is -1.666666667z.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667z + 0.6944444447 + z2 = -1 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667z + z2 = -1 + 0.6944444447

Combine like terms: -1 + 0.6944444447 = -0.3055555553
0.6944444447 + -1.666666667z + z2 = -0.3055555553

Factor a perfect square on the left side:
(z + -0.8333333335)(z + -0.8333333335) = -0.3055555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.