4=35t^2+740t+1207

Solution for 4=35t^2+740t+1207 equation:

Simplifying
4 = 35t2 + 740t + 1207

Reorder the terms:
4 = 1207 + 740t + 35t2

Solving
4 = 1207 + 740t + 35t2

Solving for variable 't'.

Combine like terms: 4 + -1207 = -1203
-1203 + -740t + -35t2 = 1207 + 740t + 35t2 + -1207 + -740t + -35t2

Reorder the terms:
-1203 + -740t + -35t2 = 1207 + -1207 + 740t + -740t + 35t2 + -35t2

Combine like terms: 1207 + -1207 = 0
-1203 + -740t + -35t2 = 0 + 740t + -740t + 35t2 + -35t2
-1203 + -740t + -35t2 = 740t + -740t + 35t2 + -35t2

Combine like terms: 740t + -740t = 0
-1203 + -740t + -35t2 = 0 + 35t2 + -35t2
-1203 + -740t + -35t2 = 35t2 + -35t2

Combine like terms: 35t2 + -35t2 = 0
-1203 + -740t + -35t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1203 + 740t + 35t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1203 + 740t + 35t2)' equal to zero and attempt to solve:

Simplifying
1203 + 740t + 35t2 = 0

Solving
1203 + 740t + 35t2 = 0

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

Divide each side by '35'.
34.37142857 + 21.14285714t + t2 = 0

Move the constant term to the right:

Add '-34.37142857' to each side of the equation.
34.37142857 + 21.14285714t + -34.37142857 + t2 = 0 + -34.37142857

Reorder the terms:
34.37142857 + -34.37142857 + 21.14285714t + t2 = 0 + -34.37142857

Combine like terms: 34.37142857 + -34.37142857 = 0.00000000
0.00000000 + 21.14285714t + t2 = 0 + -34.37142857
21.14285714t + t2 = 0 + -34.37142857

Combine like terms: 0 + -34.37142857 = -34.37142857
21.14285714t + t2 = -34.37142857

The t term is 21.14285714t.  Take half its coefficient (10.57142857).
Square it (111.7551020) and add it to both sides.

Add '111.7551020' to each side of the equation.
21.14285714t + 111.7551020 + t2 = -34.37142857 + 111.7551020

Reorder the terms:
111.7551020 + 21.14285714t + t2 = -34.37142857 + 111.7551020

Combine like terms: -34.37142857 + 111.7551020 = 77.38367343
111.7551020 + 21.14285714t + t2 = 77.38367343

Factor a perfect square on the left side:
(t + 10.57142857)(t + 10.57142857) = 77.38367343

Calculate the square root of the right side: 8.796799045

Break this problem into two subproblems by setting 
(t + 10.57142857) equal to 8.796799045 and -8.796799045.

Subproblem 1
t + 10.57142857 = 8.796799045

Simplifying
t + 10.57142857 = 8.796799045

Reorder the terms:
10.57142857 + t = 8.796799045

Solving
10.57142857 + t = 8.796799045

Solving for variable 't'.

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

Add '-10.57142857' to each side of the equation.
10.57142857 + -10.57142857 + t = 8.796799045 + -10.57142857

Combine like terms: 10.57142857 + -10.57142857 = 0.00000000
0.00000000 + t = 8.796799045 + -10.57142857
t = 8.796799045 + -10.57142857

Combine like terms: 8.796799045 + -10.57142857 = -1.774629525
t = -1.774629525

Simplifying
t = -1.774629525

Subproblem 2
t + 10.57142857 = -8.796799045

Simplifying
t + 10.57142857 = -8.796799045

Reorder the terms:
10.57142857 + t = -8.796799045

Solving
10.57142857 + t = -8.796799045

Solving for variable 't'.

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

Add '-10.57142857' to each side of the equation.
10.57142857 + -10.57142857 + t = -8.796799045 + -10.57142857

Combine like terms: 10.57142857 + -10.57142857 = 0.00000000
0.00000000 + t = -8.796799045 + -10.57142857
t = -8.796799045 + -10.57142857

Combine like terms: -8.796799045 + -10.57142857 = -19.368227615
t = -19.368227615

Simplifying
t = -19.368227615

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.774629525, -19.368227615}
Solution
t = {-1.774629525, -19.368227615}