3t^2+14t-12=0

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Solution for 3t^2+14t-12=0 equation:


Simplifying
3t2 + 14t + -12 = 0

Reorder the terms:
-12 + 14t + 3t2 = 0

Solving
-12 + 14t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
-4 + 4.666666667t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 4.666666667t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 4.666666667t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 4.666666667t + t2 = 0 + 4
4.666666667t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
4.666666667t + t2 = 4

The t term is 4.666666667t.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667t + 5.444444448 + t2 = 4 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667t + t2 = 4 + 5.444444448

Combine like terms: 4 + 5.444444448 = 9.444444448
5.444444448 + 4.666666667t + t2 = 9.444444448

Factor a perfect square on the left side:
(t + 2.333333334)(t + 2.333333334) = 9.444444448

Calculate the square root of the right side: 3.073181486

Break this problem into two subproblems by setting 
(t + 2.333333334) equal to 3.073181486 and -3.073181486.

Subproblem 1

t + 2.333333334 = 3.073181486 Simplifying t + 2.333333334 = 3.073181486 Reorder the terms: 2.333333334 + t = 3.073181486 Solving 2.333333334 + t = 3.073181486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + t = 3.073181486 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + t = 3.073181486 + -2.333333334 t = 3.073181486 + -2.333333334 Combine like terms: 3.073181486 + -2.333333334 = 0.739848152 t = 0.739848152 Simplifying t = 0.739848152

Subproblem 2

t + 2.333333334 = -3.073181486 Simplifying t + 2.333333334 = -3.073181486 Reorder the terms: 2.333333334 + t = -3.073181486 Solving 2.333333334 + t = -3.073181486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + t = -3.073181486 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + t = -3.073181486 + -2.333333334 t = -3.073181486 + -2.333333334 Combine like terms: -3.073181486 + -2.333333334 = -5.40651482 t = -5.40651482 Simplifying t = -5.40651482

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.739848152, -5.40651482}

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