3r^2-8r+7=0

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Solution for 3r^2-8r+7=0 equation: 


Simplifying
3r2 + -8r + 7 = 0

Reorder the terms:
7 + -8r + 3r2 = 0

Solving
7 + -8r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
2.333333333 + -2.666666667r + r2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -2.666666667r + -2.333333333 + r2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -2.666666667r + r2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -2.666666667r + r2 = 0 + -2.333333333
-2.666666667r + r2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-2.666666667r + r2 = -2.333333333

The r term is -2.666666667r.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667r + 1.777777780 + r2 = -2.333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667r + r2 = -2.333333333 + 1.777777780

Combine like terms: -2.333333333 + 1.777777780 = -0.555555553
1.777777780 + -2.666666667r + r2 = -0.555555553

Factor a perfect square on the left side:
(r + -1.333333334)(r + -1.333333334) = -0.555555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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