4r^2-3r+6=0

Solution for 4r^2-3r+6=0 equation:

Simplifying
4r2 + -3r + 6 = 0

Reorder the terms:
6 + -3r + 4r2 = 0

Solving
6 + -3r + 4r2 = 0

Solving for variable 'r'.

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

Divide each side by '4'.
1.5 + -0.75r + r2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.75r + -1.5 + r2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.75r + r2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.75r + r2 = 0 + -1.5
-0.75r + r2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.75r + r2 = -1.5

The r term is -0.75r.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75r + 0.140625 + r2 = -1.5 + 0.140625

Reorder the terms:
0.140625 + -0.75r + r2 = -1.5 + 0.140625

Combine like terms: -1.5 + 0.140625 = -1.359375
0.140625 + -0.75r + r2 = -1.359375

Factor a perfect square on the left side:
(r + -0.375)(r + -0.375) = -1.359375

Can't calculate square root of the right side.

The solution to this equation could not be determined.