3d^2+20d-25=0

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Solution for 3d^2+20d-25=0 equation: 


Simplifying
3d2 + 20d + -25 = 0

Reorder the terms:
-25 + 20d + 3d2 = 0

Solving
-25 + 20d + 3d2 = 0

Solving for variable 'd'.

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

Divide each side by '3'.
-8.333333333 + 6.666666667d + d2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 6.666666667d + 8.333333333 + d2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 6.666666667d + d2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 6.666666667d + d2 = 0 + 8.333333333
6.666666667d + d2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
6.666666667d + d2 = 8.333333333

The d term is 6.666666667d.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667d + 11.11111112 + d2 = 8.333333333 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667d + d2 = 8.333333333 + 11.11111112

Combine like terms: 8.333333333 + 11.11111112 = 19.444444453
11.11111112 + 6.666666667d + d2 = 19.444444453

Factor a perfect square on the left side:
(d + 3.333333334)(d + 3.333333334) = 19.444444453

Calculate the square root of the right side: 4.409585519

Break this problem into two subproblems by setting 
(d + 3.333333334) equal to 4.409585519 and -4.409585519.


Subproblem 1
d + 3.333333334 = 4.409585519

Simplifying
d + 3.333333334 = 4.409585519

Reorder the terms:
3.333333334 + d = 4.409585519

Solving
3.333333334 + d = 4.409585519

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + d = 4.409585519 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + d = 4.409585519 + -3.333333334
d = 4.409585519 + -3.333333334

Combine like terms: 4.409585519 + -3.333333334 = 1.076252185
d = 1.076252185

Simplifying
d = 1.076252185


Subproblem 2
d + 3.333333334 = -4.409585519

Simplifying
d + 3.333333334 = -4.409585519

Reorder the terms:
3.333333334 + d = -4.409585519

Solving
3.333333334 + d = -4.409585519

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + d = -4.409585519 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + d = -4.409585519 + -3.333333334
d = -4.409585519 + -3.333333334

Combine like terms: -4.409585519 + -3.333333334 = -7.742918853
d = -7.742918853

Simplifying
d = -7.742918853


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.076252185, -7.742918853}

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