3t^2+10t-12=0

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Solution for 3t^2+10t-12=0 equation:


Simplifying
3t2 + 10t + -12 = 0

Reorder the terms:
-12 + 10t + 3t2 = 0

Solving
-12 + 10t + 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 + 3.333333333t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 3.333333333t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 3.333333333t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3.333333333t + t2 = 0 + 4
3.333333333t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
3.333333333t + t2 = 4

The t term is 3.333333333t.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333t + 2.777777779 + t2 = 4 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333t + t2 = 4 + 2.777777779

Combine like terms: 4 + 2.777777779 = 6.777777779
2.777777779 + 3.333333333t + t2 = 6.777777779

Factor a perfect square on the left side:
(t + 1.666666667)(t + 1.666666667) = 6.777777779

Calculate the square root of the right side: 2.603416559

Break this problem into two subproblems by setting 
(t + 1.666666667) equal to 2.603416559 and -2.603416559.

Subproblem 1

t + 1.666666667 = 2.603416559 Simplifying t + 1.666666667 = 2.603416559 Reorder the terms: 1.666666667 + t = 2.603416559 Solving 1.666666667 + t = 2.603416559 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + t = 2.603416559 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + t = 2.603416559 + -1.666666667 t = 2.603416559 + -1.666666667 Combine like terms: 2.603416559 + -1.666666667 = 0.936749892 t = 0.936749892 Simplifying t = 0.936749892

Subproblem 2

t + 1.666666667 = -2.603416559 Simplifying t + 1.666666667 = -2.603416559 Reorder the terms: 1.666666667 + t = -2.603416559 Solving 1.666666667 + t = -2.603416559 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + t = -2.603416559 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + t = -2.603416559 + -1.666666667 t = -2.603416559 + -1.666666667 Combine like terms: -2.603416559 + -1.666666667 = -4.270083226 t = -4.270083226 Simplifying t = -4.270083226

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.936749892, -4.270083226}

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