4.9t^2+17t-300=0

Solution for 4.9t^2+17t-300=0 equation:

Simplifying
4.9t2 + 17t + -300 = 0

Reorder the terms:
-300 + 17t + 4.9t2 = 0

Solving
-300 + 17t + 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'.
-61.2244898 + 3.469387755t + t2 = 0

Move the constant term to the right:

Add '61.2244898' to each side of the equation.
-61.2244898 + 3.469387755t + 61.2244898 + t2 = 0 + 61.2244898

Reorder the terms:
-61.2244898 + 61.2244898 + 3.469387755t + t2 = 0 + 61.2244898

Combine like terms: -61.2244898 + 61.2244898 = 0.0000000
0.0000000 + 3.469387755t + t2 = 0 + 61.2244898
3.469387755t + t2 = 0 + 61.2244898

Combine like terms: 0 + 61.2244898 = 61.2244898
3.469387755t + t2 = 61.2244898

The t term is 3.469387755t.  Take half its coefficient (1.734693878).
Square it (3.009162850) and add it to both sides.

Add '3.009162850' to each side of the equation.
3.469387755t + 3.009162850 + t2 = 61.2244898 + 3.009162850

Reorder the terms:
3.009162850 + 3.469387755t + t2 = 61.2244898 + 3.009162850

Combine like terms: 61.2244898 + 3.009162850 = 64.23365265
3.009162850 + 3.469387755t + t2 = 64.23365265

Factor a perfect square on the left side:
(t + 1.734693878)(t + 1.734693878) = 64.23365265

Calculate the square root of the right side: 8.014589986

Break this problem into two subproblems by setting 
(t + 1.734693878) equal to 8.014589986 and -8.014589986.

Subproblem 1
t + 1.734693878 = 8.014589986

Simplifying
t + 1.734693878 = 8.014589986

Reorder the terms:
1.734693878 + t = 8.014589986

Solving
1.734693878 + t = 8.014589986

Solving for variable 't'.

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

Add '-1.734693878' to each side of the equation.
1.734693878 + -1.734693878 + t = 8.014589986 + -1.734693878

Combine like terms: 1.734693878 + -1.734693878 = 0.000000000
0.000000000 + t = 8.014589986 + -1.734693878
t = 8.014589986 + -1.734693878

Combine like terms: 8.014589986 + -1.734693878 = 6.279896108
t = 6.279896108

Simplifying
t = 6.279896108

Subproblem 2
t + 1.734693878 = -8.014589986

Simplifying
t + 1.734693878 = -8.014589986

Reorder the terms:
1.734693878 + t = -8.014589986

Solving
1.734693878 + t = -8.014589986

Solving for variable 't'.

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

Add '-1.734693878' to each side of the equation.
1.734693878 + -1.734693878 + t = -8.014589986 + -1.734693878

Combine like terms: 1.734693878 + -1.734693878 = 0.000000000
0.000000000 + t = -8.014589986 + -1.734693878
t = -8.014589986 + -1.734693878

Combine like terms: -8.014589986 + -1.734693878 = -9.749283864
t = -9.749283864

Simplifying
t = -9.749283864

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.279896108, -9.749283864}