4t^2-30t-14=0

Solution for 4t^2-30t-14=0 equation:

Simplifying
4t2 + -30t + -14 = 0

Reorder the terms:
-14 + -30t + 4t2 = 0

Solving
-14 + -30t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -15t + 2t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -15t + 2t2)' equal to zero and attempt to solve:

Simplifying
-7 + -15t + 2t2 = 0

Solving
-7 + -15t + 2t2 = 0

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

Divide each side by '2'.
-3.5 + -7.5t + t2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -7.5t + 3.5 + t2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -7.5t + t2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -7.5t + t2 = 0 + 3.5
-7.5t + t2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-7.5t + t2 = 3.5

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = 3.5 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = 3.5 + 14.0625

Combine like terms: 3.5 + 14.0625 = 17.5625
14.0625 + -7.5t + t2 = 17.5625

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(t + -3.75) equal to 4.190763654 and -4.190763654.

Subproblem 1
t + -3.75 = 4.190763654

Simplifying
t + -3.75 = 4.190763654

Reorder the terms:
-3.75 + t = 4.190763654

Solving
-3.75 + t = 4.190763654

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 4.190763654 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 4.190763654 + 3.75
t = 4.190763654 + 3.75

Combine like terms: 4.190763654 + 3.75 = 7.940763654
t = 7.940763654

Simplifying
t = 7.940763654

Subproblem 2
t + -3.75 = -4.190763654

Simplifying
t + -3.75 = -4.190763654

Reorder the terms:
-3.75 + t = -4.190763654

Solving
-3.75 + t = -4.190763654

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -4.190763654 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -4.190763654 + 3.75
t = -4.190763654 + 3.75

Combine like terms: -4.190763654 + 3.75 = -0.440763654
t = -0.440763654

Simplifying
t = -0.440763654

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.940763654, -0.440763654}
Solution
t = {7.940763654, -0.440763654}