225t^2+4.9t-620=0

Solution for 225t^2+4.9t-620=0 equation:

Simplifying
225t2 + 4.9t + -620 = 0

Reorder the terms:
-620 + 4.9t + 225t2 = 0

Solving
-620 + 4.9t + 225t2 = 0

Solving for variable 't'.

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

Divide each side by '225'.
-2.755555556 + 0.02177777778t + t2 = 0

Move the constant term to the right:

Add '2.755555556' to each side of the equation.
-2.755555556 + 0.02177777778t + 2.755555556 + t2 = 0 + 2.755555556

Reorder the terms:
-2.755555556 + 2.755555556 + 0.02177777778t + t2 = 0 + 2.755555556

Combine like terms: -2.755555556 + 2.755555556 = 0.000000000
0.000000000 + 0.02177777778t + t2 = 0 + 2.755555556
0.02177777778t + t2 = 0 + 2.755555556

Combine like terms: 0 + 2.755555556 = 2.755555556
0.02177777778t + t2 = 2.755555556

The t term is 0.02177777778t.  Take half its coefficient (0.01088888889).
Square it (0.0001185679013) and add it to both sides.

Add '0.0001185679013' to each side of the equation.
0.02177777778t + 0.0001185679013 + t2 = 2.755555556 + 0.0001185679013

Reorder the terms:
0.0001185679013 + 0.02177777778t + t2 = 2.755555556 + 0.0001185679013

Combine like terms: 2.755555556 + 0.0001185679013 = 2.7556741239013
0.0001185679013 + 0.02177777778t + t2 = 2.7556741239013

Factor a perfect square on the left side:
(t + 0.01088888889)(t + 0.01088888889) = 2.7556741239013

Calculate the square root of the right side: 1.660022326

Break this problem into two subproblems by setting 
(t + 0.01088888889) equal to 1.660022326 and -1.660022326.

Subproblem 1
t + 0.01088888889 = 1.660022326

Simplifying
t + 0.01088888889 = 1.660022326

Reorder the terms:
0.01088888889 + t = 1.660022326

Solving
0.01088888889 + t = 1.660022326

Solving for variable 't'.

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

Add '-0.01088888889' to each side of the equation.
0.01088888889 + -0.01088888889 + t = 1.660022326 + -0.01088888889

Combine like terms: 0.01088888889 + -0.01088888889 = 0.00000000000
0.00000000000 + t = 1.660022326 + -0.01088888889
t = 1.660022326 + -0.01088888889

Combine like terms: 1.660022326 + -0.01088888889 = 1.64913343711
t = 1.64913343711

Simplifying
t = 1.64913343711

Subproblem 2
t + 0.01088888889 = -1.660022326

Simplifying
t + 0.01088888889 = -1.660022326

Reorder the terms:
0.01088888889 + t = -1.660022326

Solving
0.01088888889 + t = -1.660022326

Solving for variable 't'.

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

Add '-0.01088888889' to each side of the equation.
0.01088888889 + -0.01088888889 + t = -1.660022326 + -0.01088888889

Combine like terms: 0.01088888889 + -0.01088888889 = 0.00000000000
0.00000000000 + t = -1.660022326 + -0.01088888889
t = -1.660022326 + -0.01088888889

Combine like terms: -1.660022326 + -0.01088888889 = -1.67091121489
t = -1.67091121489

Simplifying
t = -1.67091121489

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.64913343711, -1.67091121489}