7r^2=3r-5

Solution for 7r^2=3r-5 equation:

Simplifying
7r2 = 3r + -5

Reorder the terms:
7r2 = -5 + 3r

Solving
7r2 = -5 + 3r

Solving for variable 'r'.

Reorder the terms:
5 + -3r + 7r2 = -5 + 3r + 5 + -3r

Reorder the terms:
5 + -3r + 7r2 = -5 + 5 + 3r + -3r

Combine like terms: -5 + 5 = 0
5 + -3r + 7r2 = 0 + 3r + -3r
5 + -3r + 7r2 = 3r + -3r

Combine like terms: 3r + -3r = 0
5 + -3r + 7r2 = 0

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

Divide each side by '7'.
0.7142857143 + -0.4285714286r + r2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -0.4285714286r + -0.7142857143 + r2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -0.4285714286r + r2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -0.4285714286r + r2 = 0 + -0.7142857143
-0.4285714286r + r2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-0.4285714286r + r2 = -0.7142857143

The r term is -0.4285714286r.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286r + 0.04591836735 + r2 = -0.7142857143 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286r + r2 = -0.7142857143 + 0.04591836735

Combine like terms: -0.7142857143 + 0.04591836735 = -0.66836734695
0.04591836735 + -0.4285714286r + r2 = -0.66836734695

Factor a perfect square on the left side:
(r + -0.2142857143)(r + -0.2142857143) = -0.66836734695

Can't calculate square root of the right side.

The solution to this equation could not be determined.