t^2+3t-20=0

Solution for t^2+3t-20=0 equation:

Simplifying
t2 + 3t + -20 = 0

Reorder the terms:
-20 + 3t + t2 = 0

Solving
-20 + 3t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 3t + 20 + t2 = 0 + 20

Reorder the terms:
-20 + 20 + 3t + t2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3t + t2 = 0 + 20
3t + t2 = 0 + 20

Combine like terms: 0 + 20 = 20
3t + t2 = 20

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 = 20 + 2.25

Reorder the terms:
2.25 + 3t + t2 = 20 + 2.25

Combine like terms: 20 + 2.25 = 22.25
2.25 + 3t + t2 = 22.25

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(t + 1.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
t + 1.5 = 4.716990566

Simplifying
t + 1.5 = 4.716990566

Reorder the terms:
1.5 + t = 4.716990566

Solving
1.5 + t = 4.716990566

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 4.716990566 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 4.716990566 + -1.5
t = 4.716990566 + -1.5

Combine like terms: 4.716990566 + -1.5 = 3.216990566
t = 3.216990566

Simplifying
t = 3.216990566

Subproblem 2
t + 1.5 = -4.716990566

Simplifying
t + 1.5 = -4.716990566

Reorder the terms:
1.5 + t = -4.716990566

Solving
1.5 + t = -4.716990566

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = -4.716990566 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -4.716990566 + -1.5
t = -4.716990566 + -1.5

Combine like terms: -4.716990566 + -1.5 = -6.216990566
t = -6.216990566

Simplifying
t = -6.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.216990566, -6.216990566}