90=2t^2-2t

Solution for 90=2t^2-2t equation:

Simplifying
90 = 2t2 + -2t

Reorder the terms:
90 = -2t + 2t2

Solving
90 = -2t + 2t2

Solving for variable 't'.

Reorder the terms:
90 + 2t + -2t2 = -2t + 2t + 2t2 + -2t2

Combine like terms: -2t + 2t = 0
90 + 2t + -2t2 = 0 + 2t2 + -2t2
90 + 2t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
90 + 2t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + t + -1t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(45 + t + -1t2)' equal to zero and attempt to solve:

Simplifying
45 + t + -1t2 = 0

Solving
45 + t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-45 + -1t + t2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -1t + 45 + t2 = 0 + 45

Reorder the terms:
-45 + 45 + -1t + t2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -1t + t2 = 0 + 45
-1t + t2 = 0 + 45

Combine like terms: 0 + 45 = 45
-1t + t2 = 45

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 45 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 45 + 0.25

Combine like terms: 45 + 0.25 = 45.25
0.25 + -1t + t2 = 45.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(t + 0.5) equal to 6.726812024 and -6.726812024.

Subproblem 1
t + 0.5 = 6.726812024

Simplifying
t + 0.5 = 6.726812024

Reorder the terms:
0.5 + t = 6.726812024

Solving
0.5 + t = 6.726812024

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 6.726812024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 6.726812024 + -0.5
t = 6.726812024 + -0.5

Combine like terms: 6.726812024 + -0.5 = 6.226812024
t = 6.226812024

Simplifying
t = 6.226812024

Subproblem 2
t + 0.5 = -6.726812024

Simplifying
t + 0.5 = -6.726812024

Reorder the terms:
0.5 + t = -6.726812024

Solving
0.5 + t = -6.726812024

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -6.726812024 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -6.726812024 + -0.5
t = -6.726812024 + -0.5

Combine like terms: -6.726812024 + -0.5 = -7.226812024
t = -7.226812024

Simplifying
t = -7.226812024

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.226812024, -7.226812024}
Solution
t = {6.226812024, -7.226812024}