50t^2+100t-90=0

Solution for 50t^2+100t-90=0 equation:

Simplifying
50t2 + 100t + -90 = 0

Reorder the terms:
-90 + 100t + 50t2 = 0

Solving
-90 + 100t + 50t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-9 + 10t + 5t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-9 + 10t + 5t2)' equal to zero and attempt to solve:

Simplifying
-9 + 10t + 5t2 = 0

Solving
-9 + 10t + 5t2 = 0

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

Divide each side by '5'.
-1.8 + 2t + t2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 2t + 1.8 + t2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 2t + t2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 2t + t2 = 0 + 1.8
2t + t2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
2t + t2 = 1.8

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 1.8 + 1

Reorder the terms:
1 + 2t + t2 = 1.8 + 1

Combine like terms: 1.8 + 1 = 2.8
1 + 2t + t2 = 2.8

Factor a perfect square on the left side:
(t + 1)(t + 1) = 2.8

Calculate the square root of the right side: 1.673320053

Break this problem into two subproblems by setting 
(t + 1) equal to 1.673320053 and -1.673320053.

Subproblem 1
t + 1 = 1.673320053

Simplifying
t + 1 = 1.673320053

Reorder the terms:
1 + t = 1.673320053

Solving
1 + t = 1.673320053

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 1.673320053 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.673320053 + -1
t = 1.673320053 + -1

Combine like terms: 1.673320053 + -1 = 0.673320053
t = 0.673320053

Simplifying
t = 0.673320053

Subproblem 2
t + 1 = -1.673320053

Simplifying
t + 1 = -1.673320053

Reorder the terms:
1 + t = -1.673320053

Solving
1 + t = -1.673320053

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -1.673320053 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.673320053 + -1
t = -1.673320053 + -1

Combine like terms: -1.673320053 + -1 = -2.673320053
t = -2.673320053

Simplifying
t = -2.673320053

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.673320053, -2.673320053}
Solution
t = {0.673320053, -2.673320053}