-4.9t^2+15t-9=0

Solution for -4.9t^2+15t-9=0 equation:

Simplifying
-4.9t2 + 15t + -9 = 0

Reorder the terms:
-9 + 15t + -4.9t2 = 0

Solving
-9 + 15t + -4.9t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
1.836734694 + -3.06122449t + t2 = 0

Move the constant term to the right:

Add '-1.836734694' to each side of the equation.
1.836734694 + -3.06122449t + -1.836734694 + t2 = 0 + -1.836734694

Reorder the terms:
1.836734694 + -1.836734694 + -3.06122449t + t2 = 0 + -1.836734694

Combine like terms: 1.836734694 + -1.836734694 = 0.000000000
0.000000000 + -3.06122449t + t2 = 0 + -1.836734694
-3.06122449t + t2 = 0 + -1.836734694

Combine like terms: 0 + -1.836734694 = -1.836734694
-3.06122449t + t2 = -1.836734694

The t term is -3.06122449t.  Take half its coefficient (-1.530612245).
Square it (2.342773845) and add it to both sides.

Add '2.342773845' to each side of the equation.
-3.06122449t + 2.342773845 + t2 = -1.836734694 + 2.342773845

Reorder the terms:
2.342773845 + -3.06122449t + t2 = -1.836734694 + 2.342773845

Combine like terms: -1.836734694 + 2.342773845 = 0.506039151
2.342773845 + -3.06122449t + t2 = 0.506039151

Factor a perfect square on the left side:
(t + -1.530612245)(t + -1.530612245) = 0.506039151

Calculate the square root of the right side: 0.711364289

Break this problem into two subproblems by setting 
(t + -1.530612245) equal to 0.711364289 and -0.711364289.

Subproblem 1
t + -1.530612245 = 0.711364289

Simplifying
t + -1.530612245 = 0.711364289

Reorder the terms:
-1.530612245 + t = 0.711364289

Solving
-1.530612245 + t = 0.711364289

Solving for variable 't'.

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

Add '1.530612245' to each side of the equation.
-1.530612245 + 1.530612245 + t = 0.711364289 + 1.530612245

Combine like terms: -1.530612245 + 1.530612245 = 0.000000000
0.000000000 + t = 0.711364289 + 1.530612245
t = 0.711364289 + 1.530612245

Combine like terms: 0.711364289 + 1.530612245 = 2.241976534
t = 2.241976534

Simplifying
t = 2.241976534

Subproblem 2
t + -1.530612245 = -0.711364289

Simplifying
t + -1.530612245 = -0.711364289

Reorder the terms:
-1.530612245 + t = -0.711364289

Solving
-1.530612245 + t = -0.711364289

Solving for variable 't'.

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

Add '1.530612245' to each side of the equation.
-1.530612245 + 1.530612245 + t = -0.711364289 + 1.530612245

Combine like terms: -1.530612245 + 1.530612245 = 0.000000000
0.000000000 + t = -0.711364289 + 1.530612245
t = -0.711364289 + 1.530612245

Combine like terms: -0.711364289 + 1.530612245 = 0.819247956
t = 0.819247956

Simplifying
t = 0.819247956

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.241976534, 0.819247956}