6z^2-7z+3=0

Solution for 6z^2-7z+3=0 equation:

Simplifying
6z2 + -7z + 3 = 0

Reorder the terms:
3 + -7z + 6z2 = 0

Solving
3 + -7z + 6z2 = 0

Solving for variable 'z'.

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

Divide each side by '6'.
0.5 + -1.166666667z + z2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.166666667z + -0.5 + z2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.166666667z + z2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.166666667z + z2 = 0 + -0.5
-1.166666667z + z2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.166666667z + z2 = -0.5

The z term is -1.166666667z.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667z + 0.3402777780 + z2 = -0.5 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667z + z2 = -0.5 + 0.3402777780

Combine like terms: -0.5 + 0.3402777780 = -0.159722222
0.3402777780 + -1.166666667z + z2 = -0.159722222

Factor a perfect square on the left side:
(z + -0.5833333335)(z + -0.5833333335) = -0.159722222

Can't calculate square root of the right side.

The solution to this equation could not be determined.