t(t+1)=3t^2+5

Solution for t(t+1)=3t^2+5 equation:

Simplifying
t(t + 1) = 3t2 + 5

Reorder the terms:
t(1 + t) = 3t2 + 5
(1 * t + t * t) = 3t2 + 5
(1t + t2) = 3t2 + 5

Reorder the terms:
1t + t2 = 5 + 3t2

Solving
1t + t2 = 5 + 3t2

Solving for variable 't'.

Reorder the terms:
-5 + 1t + t2 + -3t2 = 5 + 3t2 + -5 + -3t2

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

Reorder the terms:
-5 + 1t + -2t2 = 5 + -5 + 3t2 + -3t2

Combine like terms: 5 + -5 = 0
-5 + 1t + -2t2 = 0 + 3t2 + -3t2
-5 + 1t + -2t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-5 + 1t + -2t2 = 0

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

Divide each side by '-2'.
2.5 + -0.5t + t2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -0.5t + -2.5 + t2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -0.5t + t2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -0.5t + t2 = 0 + -2.5
-0.5t + t2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-0.5t + t2 = -2.5

The t term is -0.5t.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5t + 0.0625 + t2 = -2.5 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = -2.5 + 0.0625

Combine like terms: -2.5 + 0.0625 = -2.4375
0.0625 + -0.5t + t2 = -2.4375

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = -2.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.