-15T^2+90T-85=0

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Solution for -15T^2+90T-85=0 equation: 


Simplifying
-15T2 + 90T + -85 = 0

Reorder the terms:
-85 + 90T + -15T2 = 0

Solving
-85 + 90T + -15T2 = 0

Solving for variable 'T'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-17 + 18T + -3T2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-17 + 18T + -3T2)' equal to zero and attempt to solve:

Simplifying
-17 + 18T + -3T2 = 0

Solving
-17 + 18T + -3T2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
5.666666667 + -6T + T2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -6T + -5.666666667 + T2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -6T + T2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -6T + T2 = 0 + -5.666666667
-6T + T2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-6T + T2 = -5.666666667

The T term is -6T.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6T + 9 + T2 = -5.666666667 + 9

Reorder the terms:
9 + -6T + T2 = -5.666666667 + 9

Combine like terms: -5.666666667 + 9 = 3.333333333
9 + -6T + T2 = 3.333333333

Factor a perfect square on the left side:
(T + -3)(T + -3) = 3.333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(T + -3) equal to 1.825741858 and -1.825741858.


Subproblem 1
T + -3 = 1.825741858

Simplifying
T + -3 = 1.825741858

Reorder the terms:
-3 + T = 1.825741858

Solving
-3 + T = 1.825741858

Solving for variable 'T'.

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

Add '3' to each side of the equation.
-3 + 3 + T = 1.825741858 + 3

Combine like terms: -3 + 3 = 0
0 + T = 1.825741858 + 3
T = 1.825741858 + 3

Combine like terms: 1.825741858 + 3 = 4.825741858
T = 4.825741858

Simplifying
T = 4.825741858


Subproblem 2
T + -3 = -1.825741858

Simplifying
T + -3 = -1.825741858

Reorder the terms:
-3 + T = -1.825741858

Solving
-3 + T = -1.825741858

Solving for variable 'T'.

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

Add '3' to each side of the equation.
-3 + 3 + T = -1.825741858 + 3

Combine like terms: -3 + 3 = 0
0 + T = -1.825741858 + 3
T = -1.825741858 + 3

Combine like terms: -1.825741858 + 3 = 1.174258142
T = 1.174258142

Simplifying
T = 1.174258142


Solution
The solution to the problem is based on the solutions
from the subproblems.
T = {4.825741858, 1.174258142}
Solution
T = {4.825741858, 1.174258142}

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