77=20t-5t^2

Solution for 77=20t-5t^2 equation:

Simplifying
77 = 20t + -5t2

Solving
77 = 20t + -5t2

Solving for variable 't'.

Reorder the terms:
77 + -20t + 5t2 = 20t + -20t + -5t2 + 5t2

Combine like terms: 20t + -20t = 0
77 + -20t + 5t2 = 0 + -5t2 + 5t2
77 + -20t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
77 + -20t + 5t2 = 0

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

Divide each side by '5'.
15.4 + -4t + t2 = 0

Move the constant term to the right:

Add '-15.4' to each side of the equation.
15.4 + -4t + -15.4 + t2 = 0 + -15.4

Reorder the terms:
15.4 + -15.4 + -4t + t2 = 0 + -15.4

Combine like terms: 15.4 + -15.4 = 0.0
0.0 + -4t + t2 = 0 + -15.4
-4t + t2 = 0 + -15.4

Combine like terms: 0 + -15.4 = -15.4
-4t + t2 = -15.4

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -15.4 + 4

Reorder the terms:
4 + -4t + t2 = -15.4 + 4

Combine like terms: -15.4 + 4 = -11.4
4 + -4t + t2 = -11.4

Factor a perfect square on the left side:
(t + -2)(t + -2) = -11.4

Can't calculate square root of the right side.

The solution to this equation could not be determined.