3r^2=2(r-7)

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Solution for 3r^2=2(r-7) equation: 


Simplifying
3r2 = 2(r + -7)

Reorder the terms:
3r2 = 2(-7 + r)
3r2 = (-7 * 2 + r * 2)
3r2 = (-14 + 2r)

Solving
3r2 = -14 + 2r

Solving for variable 'r'.

Reorder the terms:
14 + -2r + 3r2 = -14 + 2r + 14 + -2r

Reorder the terms:
14 + -2r + 3r2 = -14 + 14 + 2r + -2r

Combine like terms: -14 + 14 = 0
14 + -2r + 3r2 = 0 + 2r + -2r
14 + -2r + 3r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
14 + -2r + 3r2 = 0

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

Divide each side by '3'.
4.666666667 + -0.6666666667r + r2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + -0.6666666667r + -4.666666667 + r2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + -0.6666666667r + r2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + -0.6666666667r + r2 = 0 + -4.666666667
-0.6666666667r + r2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
-0.6666666667r + r2 = -4.666666667

The r term is -0.6666666667r.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667r + 0.1111111112 + r2 = -4.666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667r + r2 = -4.666666667 + 0.1111111112

Combine like terms: -4.666666667 + 0.1111111112 = -4.5555555558
0.1111111112 + -0.6666666667r + r2 = -4.5555555558

Factor a perfect square on the left side:
(r + -0.3333333334)(r + -0.3333333334) = -4.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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