4v^2+17v-30=0

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Solution for 4v^2+17v-30=0 equation: 


Simplifying
4v2 + 17v + -30 = 0

Reorder the terms:
-30 + 17v + 4v2 = 0

Solving
-30 + 17v + 4v2 = 0

Solving for variable 'v'.

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

Divide each side by '4'.
-7.5 + 4.25v + v2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 4.25v + 7.5 + v2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 4.25v + v2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 4.25v + v2 = 0 + 7.5
4.25v + v2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
4.25v + v2 = 7.5

The v term is 4.25v.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25v + 4.515625 + v2 = 7.5 + 4.515625

Reorder the terms:
4.515625 + 4.25v + v2 = 7.5 + 4.515625

Combine like terms: 7.5 + 4.515625 = 12.015625
4.515625 + 4.25v + v2 = 12.015625

Factor a perfect square on the left side:
(v + 2.125)(v + 2.125) = 12.015625

Calculate the square root of the right side: 3.466356156

Break this problem into two subproblems by setting 
(v + 2.125) equal to 3.466356156 and -3.466356156.


Subproblem 1
v + 2.125 = 3.466356156

Simplifying
v + 2.125 = 3.466356156

Reorder the terms:
2.125 + v = 3.466356156

Solving
2.125 + v = 3.466356156

Solving for variable 'v'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + v = 3.466356156 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + v = 3.466356156 + -2.125
v = 3.466356156 + -2.125

Combine like terms: 3.466356156 + -2.125 = 1.341356156
v = 1.341356156

Simplifying
v = 1.341356156


Subproblem 2
v + 2.125 = -3.466356156

Simplifying
v + 2.125 = -3.466356156

Reorder the terms:
2.125 + v = -3.466356156

Solving
2.125 + v = -3.466356156

Solving for variable 'v'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + v = -3.466356156 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + v = -3.466356156 + -2.125
v = -3.466356156 + -2.125

Combine like terms: -3.466356156 + -2.125 = -5.591356156
v = -5.591356156

Simplifying
v = -5.591356156


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.341356156, -5.591356156}

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