-4t^2+10t-5=0

Solution for -4t^2+10t-5=0 equation:

Simplifying
-4t2 + 10t + -5 = 0

Reorder the terms:
-5 + 10t + -4t2 = 0

Solving
-5 + 10t + -4t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1.25 + -2.5t + t2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.5t + -1.25 + t2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.5t + t2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.5t + t2 = 0 + -1.25
-2.5t + t2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.5t + t2 = -1.25

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + -2.5t + t2 = 0.3125

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(t + -1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
t + -1.25 = 0.559016994

Simplifying
t + -1.25 = 0.559016994

Reorder the terms:
-1.25 + t = 0.559016994

Solving
-1.25 + t = 0.559016994

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 0.559016994 + 1.25
t = 0.559016994 + 1.25

Combine like terms: 0.559016994 + 1.25 = 1.809016994
t = 1.809016994

Simplifying
t = 1.809016994

Subproblem 2
t + -1.25 = -0.559016994

Simplifying
t + -1.25 = -0.559016994

Reorder the terms:
-1.25 + t = -0.559016994

Solving
-1.25 + t = -0.559016994

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -0.559016994 + 1.25
t = -0.559016994 + 1.25

Combine like terms: -0.559016994 + 1.25 = 0.690983006
t = 0.690983006

Simplifying
t = 0.690983006

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.809016994, 0.690983006}