2t^2+5t-23=0

Solution for 2t^2+5t-23=0 equation:

Simplifying
2t2 + 5t + -23 = 0

Reorder the terms:
-23 + 5t + 2t2 = 0

Solving
-23 + 5t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
-11.5 + 2.5t + t2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + 2.5t + 11.5 + t2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + 2.5t + t2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + 2.5t + t2 = 0 + 11.5
2.5t + t2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
2.5t + t2 = 11.5

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 = 11.5 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = 11.5 + 1.5625

Combine like terms: 11.5 + 1.5625 = 13.0625
1.5625 + 2.5t + t2 = 13.0625

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(t + 1.25) equal to 3.614208074 and -3.614208074.

Subproblem 1
t + 1.25 = 3.614208074

Simplifying
t + 1.25 = 3.614208074

Reorder the terms:
1.25 + t = 3.614208074

Solving
1.25 + t = 3.614208074

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 = 3.614208074 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 3.614208074 + -1.25
t = 3.614208074 + -1.25

Combine like terms: 3.614208074 + -1.25 = 2.364208074
t = 2.364208074

Simplifying
t = 2.364208074

Subproblem 2
t + 1.25 = -3.614208074

Simplifying
t + 1.25 = -3.614208074

Reorder the terms:
1.25 + t = -3.614208074

Solving
1.25 + t = -3.614208074

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 = -3.614208074 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -3.614208074 + -1.25
t = -3.614208074 + -1.25

Combine like terms: -3.614208074 + -1.25 = -4.864208074
t = -4.864208074

Simplifying
t = -4.864208074

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.364208074, -4.864208074}