5t^2-10t=-4

Solution for 5t^2-10t=-4 equation:

Simplifying
5t2 + -10t = -4

Reorder the terms:
-10t + 5t2 = -4

Solving
-10t + 5t2 = -4

Solving for variable 't'.

Reorder the terms:
4 + -10t + 5t2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + -10t + 5t2 = 0

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

Divide each side by '5'.
0.8 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -2t + -0.8 + t2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -2t + t2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -2t + t2 = 0 + -0.8
-2t + t2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-2t + t2 = -0.8

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 = -0.8 + 1

Reorder the terms:
1 + -2t + t2 = -0.8 + 1

Combine like terms: -0.8 + 1 = 0.2
1 + -2t + t2 = 0.2

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(t + -1) equal to 0.447213596 and -0.447213596.

Subproblem 1
t + -1 = 0.447213596

Simplifying
t + -1 = 0.447213596

Reorder the terms:
-1 + t = 0.447213596

Solving
-1 + t = 0.447213596

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 = 0.447213596 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.447213596 + 1
t = 0.447213596 + 1

Combine like terms: 0.447213596 + 1 = 1.447213596
t = 1.447213596

Simplifying
t = 1.447213596

Subproblem 2
t + -1 = -0.447213596

Simplifying
t + -1 = -0.447213596

Reorder the terms:
-1 + t = -0.447213596

Solving
-1 + t = -0.447213596

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 = -0.447213596 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.447213596 + 1
t = -0.447213596 + 1

Combine like terms: -0.447213596 + 1 = 0.552786404
t = 0.552786404

Simplifying
t = 0.552786404

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.447213596, 0.552786404}