5t^2-24t-20=0

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Solution for 5t^2-24t-20=0 equation:


Simplifying
5t2 + -24t + -20 = 0

Reorder the terms:
-20 + -24t + 5t2 = 0

Solving
-20 + -24t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-4 + -4.8t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -4.8t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + -4.8t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -4.8t + t2 = 0 + 4
-4.8t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
-4.8t + t2 = 4

The t term is -4.8t.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8t + 5.76 + t2 = 4 + 5.76

Reorder the terms:
5.76 + -4.8t + t2 = 4 + 5.76

Combine like terms: 4 + 5.76 = 9.76
5.76 + -4.8t + t2 = 9.76

Factor a perfect square on the left side:
(t + -2.4)(t + -2.4) = 9.76

Calculate the square root of the right side: 3.12409987

Break this problem into two subproblems by setting 
(t + -2.4) equal to 3.12409987 and -3.12409987.

Subproblem 1

t + -2.4 = 3.12409987 Simplifying t + -2.4 = 3.12409987 Reorder the terms: -2.4 + t = 3.12409987 Solving -2.4 + t = 3.12409987 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + t = 3.12409987 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + t = 3.12409987 + 2.4 t = 3.12409987 + 2.4 Combine like terms: 3.12409987 + 2.4 = 5.52409987 t = 5.52409987 Simplifying t = 5.52409987

Subproblem 2

t + -2.4 = -3.12409987 Simplifying t + -2.4 = -3.12409987 Reorder the terms: -2.4 + t = -3.12409987 Solving -2.4 + t = -3.12409987 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + t = -3.12409987 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + t = -3.12409987 + 2.4 t = -3.12409987 + 2.4 Combine like terms: -3.12409987 + 2.4 = -0.72409987 t = -0.72409987 Simplifying t = -0.72409987

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.52409987, -0.72409987}

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