4n^2+25n-20=0

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Solution for 4n^2+25n-20=0 equation: 


Simplifying
4n2 + 25n + -20 = 0

Reorder the terms:
-20 + 25n + 4n2 = 0

Solving
-20 + 25n + 4n2 = 0

Solving for variable 'n'.

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

Divide each side by '4'.
-5 + 6.25n + n2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6.25n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + 6.25n + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6.25n + n2 = 0 + 5
6.25n + n2 = 0 + 5

Combine like terms: 0 + 5 = 5
6.25n + n2 = 5

The n term is 6.25n.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25n + 9.765625 + n2 = 5 + 9.765625

Reorder the terms:
9.765625 + 6.25n + n2 = 5 + 9.765625

Combine like terms: 5 + 9.765625 = 14.765625
9.765625 + 6.25n + n2 = 14.765625

Factor a perfect square on the left side:
(n + 3.125)(n + 3.125) = 14.765625

Calculate the square root of the right side: 3.842606537

Break this problem into two subproblems by setting 
(n + 3.125) equal to 3.842606537 and -3.842606537.


Subproblem 1
n + 3.125 = 3.842606537

Simplifying
n + 3.125 = 3.842606537

Reorder the terms:
3.125 + n = 3.842606537

Solving
3.125 + n = 3.842606537

Solving for variable 'n'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + n = 3.842606537 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + n = 3.842606537 + -3.125
n = 3.842606537 + -3.125

Combine like terms: 3.842606537 + -3.125 = 0.717606537
n = 0.717606537

Simplifying
n = 0.717606537


Subproblem 2
n + 3.125 = -3.842606537

Simplifying
n + 3.125 = -3.842606537

Reorder the terms:
3.125 + n = -3.842606537

Solving
3.125 + n = -3.842606537

Solving for variable 'n'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + n = -3.842606537 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + n = -3.842606537 + -3.125
n = -3.842606537 + -3.125

Combine like terms: -3.842606537 + -3.125 = -6.967606537
n = -6.967606537

Simplifying
n = -6.967606537


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.717606537, -6.967606537}

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