70t^2+140t-120=0

Solution for 70t^2+140t-120=0 equation:

Simplifying
70t2 + 140t + -120 = 0

Reorder the terms:
-120 + 140t + 70t2 = 0

Solving
-120 + 140t + 70t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-12 + 14t + 7t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-12 + 14t + 7t2)' equal to zero and attempt to solve:

Simplifying
-12 + 14t + 7t2 = 0

Solving
-12 + 14t + 7t2 = 0

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

Divide each side by '7'.
-1.714285714 + 2t + t2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + 2t + 1.714285714 + t2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + 2t + t2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + 2t + t2 = 0 + 1.714285714
2t + t2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
2t + t2 = 1.714285714

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 1.714285714 + 1

Reorder the terms:
1 + 2t + t2 = 1.714285714 + 1

Combine like terms: 1.714285714 + 1 = 2.714285714
1 + 2t + t2 = 2.714285714

Factor a perfect square on the left side:
(t + 1)(t + 1) = 2.714285714

Calculate the square root of the right side: 1.647508942

Break this problem into two subproblems by setting 
(t + 1) equal to 1.647508942 and -1.647508942.

Subproblem 1
t + 1 = 1.647508942

Simplifying
t + 1 = 1.647508942

Reorder the terms:
1 + t = 1.647508942

Solving
1 + t = 1.647508942

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 1.647508942 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.647508942 + -1
t = 1.647508942 + -1

Combine like terms: 1.647508942 + -1 = 0.647508942
t = 0.647508942

Simplifying
t = 0.647508942

Subproblem 2
t + 1 = -1.647508942

Simplifying
t + 1 = -1.647508942

Reorder the terms:
1 + t = -1.647508942

Solving
1 + t = -1.647508942

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -1.647508942 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.647508942 + -1
t = -1.647508942 + -1

Combine like terms: -1.647508942 + -1 = -2.647508942
t = -2.647508942

Simplifying
t = -2.647508942

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.647508942, -2.647508942}
Solution
t = {0.647508942, -2.647508942}