5t^2+20t-18=0

Solution for 5t^2+20t-18=0 equation:

Simplifying
5t2 + 20t + -18 = 0

Reorder the terms:
-18 + 20t + 5t2 = 0

Solving
-18 + 20t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-3.6 + 4t + t2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 4t + 3.6 + t2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 4t + t2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 4t + t2 = 0 + 3.6
4t + t2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
4t + t2 = 3.6

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = 3.6 + 4

Reorder the terms:
4 + 4t + t2 = 3.6 + 4

Combine like terms: 3.6 + 4 = 7.6
4 + 4t + t2 = 7.6

Factor a perfect square on the left side:
(t + 2)(t + 2) = 7.6

Calculate the square root of the right side: 2.75680975

Break this problem into two subproblems by setting 
(t + 2) equal to 2.75680975 and -2.75680975.

Subproblem 1
t + 2 = 2.75680975

Simplifying
t + 2 = 2.75680975

Reorder the terms:
2 + t = 2.75680975

Solving
2 + t = 2.75680975

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 2.75680975 + -2

Combine like terms: 2 + -2 = 0
0 + t = 2.75680975 + -2
t = 2.75680975 + -2

Combine like terms: 2.75680975 + -2 = 0.75680975
t = 0.75680975

Simplifying
t = 0.75680975

Subproblem 2
t + 2 = -2.75680975

Simplifying
t + 2 = -2.75680975

Reorder the terms:
2 + t = -2.75680975

Solving
2 + t = -2.75680975

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -2.75680975 + -2

Combine like terms: 2 + -2 = 0
0 + t = -2.75680975 + -2
t = -2.75680975 + -2

Combine like terms: -2.75680975 + -2 = -4.75680975
t = -4.75680975

Simplifying
t = -4.75680975

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.75680975, -4.75680975}