24t-8t^2=90

Solution for 24t-8t^2=90 equation:

Simplifying
24t + -8t2 = 90

Solving
24t + -8t2 = 90

Solving for variable 't'.

Reorder the terms:
-90 + 24t + -8t2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 24t + -8t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 12t + -4t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + 12t + -4t2)' equal to zero and attempt to solve:

Simplifying
-45 + 12t + -4t2 = 0

Solving
-45 + 12t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
11.25 + -3t + t2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + -3t + -11.25 + t2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + -3t + t2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + -3t + t2 = 0 + -11.25
-3t + t2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
-3t + t2 = -11.25

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 = -11.25 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -11.25 + 2.25

Combine like terms: -11.25 + 2.25 = -9
2.25 + -3t + t2 = -9

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = -9

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.