5t^2-3t-4=0

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Solution for 5t^2-3t-4=0 equation:


Simplifying
5t2 + -3t + -4 = 0

Reorder the terms:
-4 + -3t + 5t2 = 0

Solving
-4 + -3t + 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'.
-0.8 + -0.6t + t2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -0.6t + 0.8 + t2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -0.6t + t2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -0.6t + t2 = 0 + 0.8
-0.6t + t2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-0.6t + t2 = 0.8

The t term is -0.6t.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6t + 0.09 + t2 = 0.8 + 0.09

Reorder the terms:
0.09 + -0.6t + t2 = 0.8 + 0.09

Combine like terms: 0.8 + 0.09 = 0.89
0.09 + -0.6t + t2 = 0.89

Factor a perfect square on the left side:
(t + -0.3)(t + -0.3) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(t + -0.3) equal to 0.943398113 and -0.943398113.

Subproblem 1

t + -0.3 = 0.943398113 Simplifying t + -0.3 = 0.943398113 Reorder the terms: -0.3 + t = 0.943398113 Solving -0.3 + t = 0.943398113 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + t = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + t = 0.943398113 + 0.3 t = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 t = 1.243398113 Simplifying t = 1.243398113

Subproblem 2

t + -0.3 = -0.943398113 Simplifying t + -0.3 = -0.943398113 Reorder the terms: -0.3 + t = -0.943398113 Solving -0.3 + t = -0.943398113 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + t = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + t = -0.943398113 + 0.3 t = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 t = -0.643398113 Simplifying t = -0.643398113

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.243398113, -0.643398113}

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