t(t+1)=3t^2+7

Solution for t(t+1)=3t^2+7 equation:

Simplifying
t(t + 1) = 3t2 + 7

Reorder the terms:
t(1 + t) = 3t2 + 7
(1 * t + t * t) = 3t2 + 7
(1t + t2) = 3t2 + 7

Reorder the terms:
1t + t2 = 7 + 3t2

Solving
1t + t2 = 7 + 3t2

Solving for variable 't'.

Reorder the terms:
-7 + 1t + t2 + -3t2 = 7 + 3t2 + -7 + -3t2

Combine like terms: t2 + -3t2 = -2t2
-7 + 1t + -2t2 = 7 + 3t2 + -7 + -3t2

Reorder the terms:
-7 + 1t + -2t2 = 7 + -7 + 3t2 + -3t2

Combine like terms: 7 + -7 = 0
-7 + 1t + -2t2 = 0 + 3t2 + -3t2
-7 + 1t + -2t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-7 + 1t + -2t2 = 0

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

Divide each side by '-2'.
3.5 + -0.5t + t2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -0.5t + -3.5 + t2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -0.5t + t2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -0.5t + t2 = 0 + -3.5
-0.5t + t2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-0.5t + t2 = -3.5

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 = -3.5 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = -3.5 + 0.0625

Combine like terms: -3.5 + 0.0625 = -3.4375
0.0625 + -0.5t + t2 = -3.4375

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = -3.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.