5r^2=3r-1

Solution for 5r^2=3r-1 equation:

Simplifying
5r2 = 3r + -1

Reorder the terms:
5r2 = -1 + 3r

Solving
5r2 = -1 + 3r

Solving for variable 'r'.

Reorder the terms:
1 + -3r + 5r2 = -1 + 3r + 1 + -3r

Reorder the terms:
1 + -3r + 5r2 = -1 + 1 + 3r + -3r

Combine like terms: -1 + 1 = 0
1 + -3r + 5r2 = 0 + 3r + -3r
1 + -3r + 5r2 = 3r + -3r

Combine like terms: 3r + -3r = 0
1 + -3r + 5r2 = 0

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

Divide each side by '5'.
0.2 + -0.6r + r2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -0.6r + -0.2 + r2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -0.6r + r2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -0.6r + r2 = 0 + -0.2
-0.6r + r2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-0.6r + r2 = -0.2

The r term is -0.6r.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6r + 0.09 + r2 = -0.2 + 0.09

Reorder the terms:
0.09 + -0.6r + r2 = -0.2 + 0.09

Combine like terms: -0.2 + 0.09 = -0.11
0.09 + -0.6r + r2 = -0.11

Factor a perfect square on the left side:
(r + -0.3)(r + -0.3) = -0.11

Can't calculate square root of the right side.

The solution to this equation could not be determined.