4.9t^2+10t-61=0

Solution for 4.9t^2+10t-61=0 equation:

Simplifying
4.9t2 + 10t + -61 = 0

Reorder the terms:
-61 + 10t + 4.9t2 = 0

Solving
-61 + 10t + 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'.
-12.44897959 + 2.040816327t + t2 = 0

Move the constant term to the right:

Add '12.44897959' to each side of the equation.
-12.44897959 + 2.040816327t + 12.44897959 + t2 = 0 + 12.44897959

Reorder the terms:
-12.44897959 + 12.44897959 + 2.040816327t + t2 = 0 + 12.44897959

Combine like terms: -12.44897959 + 12.44897959 = 0.00000000
0.00000000 + 2.040816327t + t2 = 0 + 12.44897959
2.040816327t + t2 = 0 + 12.44897959

Combine like terms: 0 + 12.44897959 = 12.44897959
2.040816327t + t2 = 12.44897959

The t term is 2.040816327t.  Take half its coefficient (1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
2.040816327t + 1.041232821 + t2 = 12.44897959 + 1.041232821

Reorder the terms:
1.041232821 + 2.040816327t + t2 = 12.44897959 + 1.041232821

Combine like terms: 12.44897959 + 1.041232821 = 13.490212411
1.041232821 + 2.040816327t + t2 = 13.490212411

Factor a perfect square on the left side:
(t + 1.020408164)(t + 1.020408164) = 13.490212411

Calculate the square root of the right side: 3.672902451

Break this problem into two subproblems by setting 
(t + 1.020408164) equal to 3.672902451 and -3.672902451.

Subproblem 1
t + 1.020408164 = 3.672902451

Simplifying
t + 1.020408164 = 3.672902451

Reorder the terms:
1.020408164 + t = 3.672902451

Solving
1.020408164 + t = 3.672902451

Solving for variable 't'.

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

Add '-1.020408164' to each side of the equation.
1.020408164 + -1.020408164 + t = 3.672902451 + -1.020408164

Combine like terms: 1.020408164 + -1.020408164 = 0.000000000
0.000000000 + t = 3.672902451 + -1.020408164
t = 3.672902451 + -1.020408164

Combine like terms: 3.672902451 + -1.020408164 = 2.652494287
t = 2.652494287

Simplifying
t = 2.652494287

Subproblem 2
t + 1.020408164 = -3.672902451

Simplifying
t + 1.020408164 = -3.672902451

Reorder the terms:
1.020408164 + t = -3.672902451

Solving
1.020408164 + t = -3.672902451

Solving for variable 't'.

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

Add '-1.020408164' to each side of the equation.
1.020408164 + -1.020408164 + t = -3.672902451 + -1.020408164

Combine like terms: 1.020408164 + -1.020408164 = 0.000000000
0.000000000 + t = -3.672902451 + -1.020408164
t = -3.672902451 + -1.020408164

Combine like terms: -3.672902451 + -1.020408164 = -4.693310615
t = -4.693310615

Simplifying
t = -4.693310615

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.652494287, -4.693310615}