4.905t^2+6.43t-2.10=0

Solution for 4.905t^2+6.43t-2.10=0 equation:

Simplifying
4.905t2 + 6.43t + -2.10 = 0

Reorder the terms:
-2.10 + 6.43t + 4.905t2 = 0

Solving
-2.10 + 6.43t + 4.905t2 = 0

Solving for variable 't'.

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

Divide each side by '4.905'.
-0.4281345566 + 1.310907238t + t2 = 0

Move the constant term to the right:

Add '0.4281345566' to each side of the equation.
-0.4281345566 + 1.310907238t + 0.4281345566 + t2 = 0 + 0.4281345566

Reorder the terms:
-0.4281345566 + 0.4281345566 + 1.310907238t + t2 = 0 + 0.4281345566

Combine like terms: -0.4281345566 + 0.4281345566 = 0.0000000000
0.0000000000 + 1.310907238t + t2 = 0 + 0.4281345566
1.310907238t + t2 = 0 + 0.4281345566

Combine like terms: 0 + 0.4281345566 = 0.4281345566
1.310907238t + t2 = 0.4281345566

The t term is 1.310907238t.  Take half its coefficient (0.655453619).
Square it (0.4296194467) and add it to both sides.

Add '0.4296194467' to each side of the equation.
1.310907238t + 0.4296194467 + t2 = 0.4281345566 + 0.4296194467

Reorder the terms:
0.4296194467 + 1.310907238t + t2 = 0.4281345566 + 0.4296194467

Combine like terms: 0.4281345566 + 0.4296194467 = 0.8577540033
0.4296194467 + 1.310907238t + t2 = 0.8577540033

Factor a perfect square on the left side:
(t + 0.655453619)(t + 0.655453619) = 0.8577540033

Calculate the square root of the right side: 0.926150098

Break this problem into two subproblems by setting 
(t + 0.655453619) equal to 0.926150098 and -0.926150098.

Subproblem 1
t + 0.655453619 = 0.926150098

Simplifying
t + 0.655453619 = 0.926150098

Reorder the terms:
0.655453619 + t = 0.926150098

Solving
0.655453619 + t = 0.926150098

Solving for variable 't'.

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

Add '-0.655453619' to each side of the equation.
0.655453619 + -0.655453619 + t = 0.926150098 + -0.655453619

Combine like terms: 0.655453619 + -0.655453619 = 0.000000000
0.000000000 + t = 0.926150098 + -0.655453619
t = 0.926150098 + -0.655453619

Combine like terms: 0.926150098 + -0.655453619 = 0.270696479
t = 0.270696479

Simplifying
t = 0.270696479

Subproblem 2
t + 0.655453619 = -0.926150098

Simplifying
t + 0.655453619 = -0.926150098

Reorder the terms:
0.655453619 + t = -0.926150098

Solving
0.655453619 + t = -0.926150098

Solving for variable 't'.

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

Add '-0.655453619' to each side of the equation.
0.655453619 + -0.655453619 + t = -0.926150098 + -0.655453619

Combine like terms: 0.655453619 + -0.655453619 = 0.000000000
0.000000000 + t = -0.926150098 + -0.655453619
t = -0.926150098 + -0.655453619

Combine like terms: -0.926150098 + -0.655453619 = -1.581603717
t = -1.581603717

Simplifying
t = -1.581603717

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.270696479, -1.581603717}