0=5t^2-15t+100

Solution for 0=5t^2-15t+100 equation:

Simplifying
0 = 5t2 + -15t + 100

Reorder the terms:
0 = 100 + -15t + 5t2

Solving
0 = 100 + -15t + 5t2

Solving for variable 't'.

Combine like terms: 0 + -100 = -100
-100 + 15t + -5t2 = 100 + -15t + 5t2 + -100 + 15t + -5t2

Reorder the terms:
-100 + 15t + -5t2 = 100 + -100 + -15t + 15t + 5t2 + -5t2

Combine like terms: 100 + -100 = 0
-100 + 15t + -5t2 = 0 + -15t + 15t + 5t2 + -5t2
-100 + 15t + -5t2 = -15t + 15t + 5t2 + -5t2

Combine like terms: -15t + 15t = 0
-100 + 15t + -5t2 = 0 + 5t2 + -5t2
-100 + 15t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-100 + 15t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + 3t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-20 + 3t + -1t2)' equal to zero and attempt to solve:

Simplifying
-20 + 3t + -1t2 = 0

Solving
-20 + 3t + -1t2 = 0

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

Divide each side by '-1'.
20 + -3t + t2 = 0

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 = -17.75
2.25 + -3t + t2 = -17.75

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = -17.75

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.