-5t^2-14t-3=0

Solution for -5t^2-14t-3=0 equation:

Simplifying
-5t2 + -14t + -3 = 0

Reorder the terms:
-3 + -14t + -5t2 = 0

Solving
-3 + -14t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 14t + 5t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 14t + 5t2)' equal to zero and attempt to solve:

Simplifying
3 + 14t + 5t2 = 0

Solving
3 + 14t + 5t2 = 0

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

Divide each side by '5'.
0.6 + 2.8t + t2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 2.8t + -0.6 + t2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 2.8t + t2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 2.8t + t2 = 0 + -0.6
2.8t + t2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
2.8t + t2 = -0.6

The t term is 2.8t.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8t + 1.96 + t2 = -0.6 + 1.96

Reorder the terms:
1.96 + 2.8t + t2 = -0.6 + 1.96

Combine like terms: -0.6 + 1.96 = 1.36
1.96 + 2.8t + t2 = 1.36

Factor a perfect square on the left side:
(t + 1.4)(t + 1.4) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(t + 1.4) equal to 1.166190379 and -1.166190379.

Subproblem 1
t + 1.4 = 1.166190379

Simplifying
t + 1.4 = 1.166190379

Reorder the terms:
1.4 + t = 1.166190379

Solving
1.4 + t = 1.166190379

Solving for variable 't'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + t = 1.166190379 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + t = 1.166190379 + -1.4
t = 1.166190379 + -1.4

Combine like terms: 1.166190379 + -1.4 = -0.233809621
t = -0.233809621

Simplifying
t = -0.233809621

Subproblem 2
t + 1.4 = -1.166190379

Simplifying
t + 1.4 = -1.166190379

Reorder the terms:
1.4 + t = -1.166190379

Solving
1.4 + t = -1.166190379

Solving for variable 't'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + t = -1.166190379 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + t = -1.166190379 + -1.4
t = -1.166190379 + -1.4

Combine like terms: -1.166190379 + -1.4 = -2.566190379
t = -2.566190379

Simplifying
t = -2.566190379

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.233809621, -2.566190379}
Solution
t = {-0.233809621, -2.566190379}