-20.4t=5.7t^2+36

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Solution for -20.4t=5.7t^2+36 equation:


Simplifying
-20.4t = 5.7t2 + 36

Reorder the terms:
-20.4t = 36 + 5.7t2

Solving
-20.4t = 36 + 5.7t2

Solving for variable 't'.

Reorder the terms:
-36 + -20.4t + -5.7t2 = 36 + 5.7t2 + -36 + -5.7t2

Reorder the terms:
-36 + -20.4t + -5.7t2 = 36 + -36 + 5.7t2 + -5.7t2

Combine like terms: 36 + -36 = 0
-36 + -20.4t + -5.7t2 = 0 + 5.7t2 + -5.7t2
-36 + -20.4t + -5.7t2 = 5.7t2 + -5.7t2

Combine like terms: 5.7t2 + -5.7t2 = 0.0
-36 + -20.4t + -5.7t2 = 0.0

Begin completing the square.  Divide all terms by
-5.7 the coefficient of the squared term: 

Divide each side by '-5.7'.
6.315789474 + 3.578947368t + t2 = 0

Move the constant term to the right:

Add '-6.315789474' to each side of the equation.
6.315789474 + 3.578947368t + -6.315789474 + t2 = 0 + -6.315789474

Reorder the terms:
6.315789474 + -6.315789474 + 3.578947368t + t2 = 0 + -6.315789474

Combine like terms: 6.315789474 + -6.315789474 = 0.000000000
0.000000000 + 3.578947368t + t2 = 0 + -6.315789474
3.578947368t + t2 = 0 + -6.315789474

Combine like terms: 0 + -6.315789474 = -6.315789474
3.578947368t + t2 = -6.315789474

The t term is 3.578947368t.  Take half its coefficient (1.789473684).
Square it (3.202216066) and add it to both sides.

Add '3.202216066' to each side of the equation.
3.578947368t + 3.202216066 + t2 = -6.315789474 + 3.202216066

Reorder the terms:
3.202216066 + 3.578947368t + t2 = -6.315789474 + 3.202216066

Combine like terms: -6.315789474 + 3.202216066 = -3.113573408
3.202216066 + 3.578947368t + t2 = -3.113573408

Factor a perfect square on the left side:
(t + 1.789473684)(t + 1.789473684) = -3.113573408

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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