0=-70+40t+5t^2

Solution for 0=-70+40t+5t^2 equation:

Simplifying
0 = -70 + 40t + 5t2

Solving
0 = -70 + 40t + 5t2

Solving for variable 't'.

Combine like terms: 0 + 70 = 70
70 + -40t + -5t2 = -70 + 40t + 5t2 + 70 + -40t + -5t2

Reorder the terms:
70 + -40t + -5t2 = -70 + 70 + 40t + -40t + 5t2 + -5t2

Combine like terms: -70 + 70 = 0
70 + -40t + -5t2 = 0 + 40t + -40t + 5t2 + -5t2
70 + -40t + -5t2 = 40t + -40t + 5t2 + -5t2

Combine like terms: 40t + -40t = 0
70 + -40t + -5t2 = 0 + 5t2 + -5t2
70 + -40t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
70 + -40t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + -8t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(14 + -8t + -1t2)' equal to zero and attempt to solve:

Simplifying
14 + -8t + -1t2 = 0

Solving
14 + -8t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-14 + 8t + t2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 8t + 14 + t2 = 0 + 14

Reorder the terms:
-14 + 14 + 8t + t2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 8t + t2 = 0 + 14
8t + t2 = 0 + 14

Combine like terms: 0 + 14 = 14
8t + t2 = 14

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = 14 + 16

Reorder the terms:
16 + 8t + t2 = 14 + 16

Combine like terms: 14 + 16 = 30
16 + 8t + t2 = 30

Factor a perfect square on the left side:
(t + 4)(t + 4) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(t + 4) equal to 5.477225575 and -5.477225575.

Subproblem 1
t + 4 = 5.477225575

Simplifying
t + 4 = 5.477225575

Reorder the terms:
4 + t = 5.477225575

Solving
4 + t = 5.477225575

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 5.477225575 + -4

Combine like terms: 4 + -4 = 0
0 + t = 5.477225575 + -4
t = 5.477225575 + -4

Combine like terms: 5.477225575 + -4 = 1.477225575
t = 1.477225575

Simplifying
t = 1.477225575

Subproblem 2
t + 4 = -5.477225575

Simplifying
t + 4 = -5.477225575

Reorder the terms:
4 + t = -5.477225575

Solving
4 + t = -5.477225575

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -5.477225575 + -4

Combine like terms: 4 + -4 = 0
0 + t = -5.477225575 + -4
t = -5.477225575 + -4

Combine like terms: -5.477225575 + -4 = -9.477225575
t = -9.477225575

Simplifying
t = -9.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.477225575, -9.477225575}
Solution
t = {1.477225575, -9.477225575}