2t^2+6t+5=0

Solution for 2t^2+6t+5=0 equation:

Simplifying
2t2 + 6t + 5 = 0

Reorder the terms:
5 + 6t + 2t2 = 0

Solving
5 + 6t + 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'.
2.5 + 3t + t2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 3t + -2.5 + t2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 3t + t2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 3t + t2 = 0 + -2.5
3t + t2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
3t + t2 = -2.5

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = -2.5 + 2.25

Reorder the terms:
2.25 + 3t + t2 = -2.5 + 2.25

Combine like terms: -2.5 + 2.25 = -0.25
2.25 + 3t + t2 = -0.25

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.