5t^2+12t-25=0

Solution for 5t^2+12t-25=0 equation:

Simplifying
5t2 + 12t + -25 = 0

Reorder the terms:
-25 + 12t + 5t2 = 0

Solving
-25 + 12t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-5 + 2.4t + t2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2.4t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + 2.4t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2.4t + t2 = 0 + 5
2.4t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
2.4t + t2 = 5

The t term is 2.4t.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4t + 1.44 + t2 = 5 + 1.44

Reorder the terms:
1.44 + 2.4t + t2 = 5 + 1.44

Combine like terms: 5 + 1.44 = 6.44
1.44 + 2.4t + t2 = 6.44

Factor a perfect square on the left side:
(t + 1.2)(t + 1.2) = 6.44

Calculate the square root of the right side: 2.537715508

Break this problem into two subproblems by setting 
(t + 1.2) equal to 2.537715508 and -2.537715508.

Subproblem 1
t + 1.2 = 2.537715508

Simplifying
t + 1.2 = 2.537715508

Reorder the terms:
1.2 + t = 2.537715508

Solving
1.2 + t = 2.537715508

Solving for variable 't'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + t = 2.537715508 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + t = 2.537715508 + -1.2
t = 2.537715508 + -1.2

Combine like terms: 2.537715508 + -1.2 = 1.337715508
t = 1.337715508

Simplifying
t = 1.337715508

Subproblem 2
t + 1.2 = -2.537715508

Simplifying
t + 1.2 = -2.537715508

Reorder the terms:
1.2 + t = -2.537715508

Solving
1.2 + t = -2.537715508

Solving for variable 't'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + t = -2.537715508 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + t = -2.537715508 + -1.2
t = -2.537715508 + -1.2

Combine like terms: -2.537715508 + -1.2 = -3.737715508
t = -3.737715508

Simplifying
t = -3.737715508

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.337715508, -3.737715508}