-5t^2+5t+2=3

Solution for -5t^2+5t+2=3 equation:

Simplifying
-5t2 + 5t + 2 = 3

Reorder the terms:
2 + 5t + -5t2 = 3

Solving
2 + 5t + -5t2 = 3

Solving for variable 't'.

Reorder the terms:
2 + -3 + 5t + -5t2 = 3 + -3

Combine like terms: 2 + -3 = -1
-1 + 5t + -5t2 = 3 + -3

Combine like terms: 3 + -3 = 0
-1 + 5t + -5t2 = 0

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

Divide each side by '-5'.
0.2 + -1t + t2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1t + -0.2 + t2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1t + t2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1t + t2 = 0 + -0.2
-1t + t2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1t + t2 = -0.2

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = -0.2 + 0.25

Reorder the terms:
0.25 + -1t + t2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
0.25 + -1t + t2 = 0.05

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(t + -0.5) equal to 0.223606798 and -0.223606798.

Subproblem 1
t + -0.5 = 0.223606798

Simplifying
t + -0.5 = 0.223606798

Reorder the terms:
-0.5 + t = 0.223606798

Solving
-0.5 + t = 0.223606798

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 0.223606798 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 0.223606798 + 0.5
t = 0.223606798 + 0.5

Combine like terms: 0.223606798 + 0.5 = 0.723606798
t = 0.723606798

Simplifying
t = 0.723606798

Subproblem 2
t + -0.5 = -0.223606798

Simplifying
t + -0.5 = -0.223606798

Reorder the terms:
-0.5 + t = -0.223606798

Solving
-0.5 + t = -0.223606798

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = -0.223606798 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -0.223606798 + 0.5
t = -0.223606798 + 0.5

Combine like terms: -0.223606798 + 0.5 = 0.276393202
t = 0.276393202

Simplifying
t = 0.276393202

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.723606798, 0.276393202}