16t^2+2.1t=20

Solution for 16t^2+2.1t=20 equation:

Simplifying
16t2 + 2.1t = 20

Reorder the terms:
2.1t + 16t2 = 20

Solving
2.1t + 16t2 = 20

Solving for variable 't'.

Reorder the terms:
-20 + 2.1t + 16t2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 2.1t + 16t2 = 0

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

Divide each side by '16'.
-1.25 + 0.13125t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.13125t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.13125t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.13125t + t2 = 0 + 1.25
0.13125t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.13125t + t2 = 1.25

The t term is 0.13125t.  Take half its coefficient (0.065625).
Square it (0.004306640625) and add it to both sides.

Add '0.004306640625' to each side of the equation.
0.13125t + 0.004306640625 + t2 = 1.25 + 0.004306640625

Reorder the terms:
0.004306640625 + 0.13125t + t2 = 1.25 + 0.004306640625

Combine like terms: 1.25 + 0.004306640625 = 1.254306640625
0.004306640625 + 0.13125t + t2 = 1.254306640625

Factor a perfect square on the left side:
(t + 0.065625)(t + 0.065625) = 1.254306640625

Calculate the square root of the right side: 1.119958321

Break this problem into two subproblems by setting 
(t + 0.065625) equal to 1.119958321 and -1.119958321.

Subproblem 1
t + 0.065625 = 1.119958321

Simplifying
t + 0.065625 = 1.119958321

Reorder the terms:
0.065625 + t = 1.119958321

Solving
0.065625 + t = 1.119958321

Solving for variable 't'.

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

Add '-0.065625' to each side of the equation.
0.065625 + -0.065625 + t = 1.119958321 + -0.065625

Combine like terms: 0.065625 + -0.065625 = 0.000000
0.000000 + t = 1.119958321 + -0.065625
t = 1.119958321 + -0.065625

Combine like terms: 1.119958321 + -0.065625 = 1.054333321
t = 1.054333321

Simplifying
t = 1.054333321

Subproblem 2
t + 0.065625 = -1.119958321

Simplifying
t + 0.065625 = -1.119958321

Reorder the terms:
0.065625 + t = -1.119958321

Solving
0.065625 + t = -1.119958321

Solving for variable 't'.

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

Add '-0.065625' to each side of the equation.
0.065625 + -0.065625 + t = -1.119958321 + -0.065625

Combine like terms: 0.065625 + -0.065625 = 0.000000
0.000000 + t = -1.119958321 + -0.065625
t = -1.119958321 + -0.065625

Combine like terms: -1.119958321 + -0.065625 = -1.185583321
t = -1.185583321

Simplifying
t = -1.185583321

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.054333321, -1.185583321}