3=5t^2+15t+20

Solution for 3=5t^2+15t+20 equation:

Simplifying
3 = 5t2 + 15t + 20

Reorder the terms:
3 = 20 + 15t + 5t2

Solving
3 = 20 + 15t + 5t2

Solving for variable 't'.

Combine like terms: 3 + -20 = -17
-17 + -15t + -5t2 = 20 + 15t + 5t2 + -20 + -15t + -5t2

Reorder the terms:
-17 + -15t + -5t2 = 20 + -20 + 15t + -15t + 5t2 + -5t2

Combine like terms: 20 + -20 = 0
-17 + -15t + -5t2 = 0 + 15t + -15t + 5t2 + -5t2
-17 + -15t + -5t2 = 15t + -15t + 5t2 + -5t2

Combine like terms: 15t + -15t = 0
-17 + -15t + -5t2 = 0 + 5t2 + -5t2
-17 + -15t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-17 + -15t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 15t + 5t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(17 + 15t + 5t2)' equal to zero and attempt to solve:

Simplifying
17 + 15t + 5t2 = 0

Solving
17 + 15t + 5t2 = 0

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

Divide each side by '5'.
3.4 + 3t + t2 = 0

Move the constant term to the right:

Add '-3.4' to each side of the equation.
3.4 + 3t + -3.4 + t2 = 0 + -3.4

Reorder the terms:
3.4 + -3.4 + 3t + t2 = 0 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
0.0 + 3t + t2 = 0 + -3.4
3t + t2 = 0 + -3.4

Combine like terms: 0 + -3.4 = -3.4
3t + t2 = -3.4

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 = -3.4 + 2.25

Reorder the terms:
2.25 + 3t + t2 = -3.4 + 2.25

Combine like terms: -3.4 + 2.25 = -1.15
2.25 + 3t + t2 = -1.15

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = -1.15

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.