16t^2-45t+30=0

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Solution for 16t^2-45t+30=0 equation:


Simplifying
16t2 + -45t + 30 = 0

Reorder the terms:
30 + -45t + 16t2 = 0

Solving
30 + -45t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
1.875 + -2.8125t + t2 = 0

Move the constant term to the right:

Add '-1.875' to each side of the equation.
1.875 + -2.8125t + -1.875 + t2 = 0 + -1.875

Reorder the terms:
1.875 + -1.875 + -2.8125t + t2 = 0 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + -2.8125t + t2 = 0 + -1.875
-2.8125t + t2 = 0 + -1.875

Combine like terms: 0 + -1.875 = -1.875
-2.8125t + t2 = -1.875

The t term is -2.8125t.  Take half its coefficient (-1.40625).
Square it (1.977539063) and add it to both sides.

Add '1.977539063' to each side of the equation.
-2.8125t + 1.977539063 + t2 = -1.875 + 1.977539063

Reorder the terms:
1.977539063 + -2.8125t + t2 = -1.875 + 1.977539063

Combine like terms: -1.875 + 1.977539063 = 0.102539063
1.977539063 + -2.8125t + t2 = 0.102539063

Factor a perfect square on the left side:
(t + -1.40625)(t + -1.40625) = 0.102539063

Calculate the square root of the right side: 0.320217212

Break this problem into two subproblems by setting 
(t + -1.40625) equal to 0.320217212 and -0.320217212.

Subproblem 1

t + -1.40625 = 0.320217212 Simplifying t + -1.40625 = 0.320217212 Reorder the terms: -1.40625 + t = 0.320217212 Solving -1.40625 + t = 0.320217212 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 0.320217212 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 0.320217212 + 1.40625 t = 0.320217212 + 1.40625 Combine like terms: 0.320217212 + 1.40625 = 1.726467212 t = 1.726467212 Simplifying t = 1.726467212

Subproblem 2

t + -1.40625 = -0.320217212 Simplifying t + -1.40625 = -0.320217212 Reorder the terms: -1.40625 + t = -0.320217212 Solving -1.40625 + t = -0.320217212 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -0.320217212 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -0.320217212 + 1.40625 t = -0.320217212 + 1.40625 Combine like terms: -0.320217212 + 1.40625 = 1.086032788 t = 1.086032788 Simplifying t = 1.086032788

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.726467212, 1.086032788}

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