3t^2=11t+4

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Solution for 3t^2=11t+4 equation:


Simplifying
3t2 = 11t + 4

Reorder the terms:
3t2 = 4 + 11t

Solving
3t2 = 4 + 11t

Solving for variable 't'.

Reorder the terms:
-4 + -11t + 3t2 = 4 + 11t + -4 + -11t

Reorder the terms:
-4 + -11t + 3t2 = 4 + -4 + 11t + -11t

Combine like terms: 4 + -4 = 0
-4 + -11t + 3t2 = 0 + 11t + -11t
-4 + -11t + 3t2 = 11t + -11t

Combine like terms: 11t + -11t = 0
-4 + -11t + 3t2 = 0

Factor a trinomial.
(-1 + -3t)(4 + -1t) = 0

Subproblem 1

Set the factor '(-1 + -3t)' equal to zero and attempt to solve: Simplifying -1 + -3t = 0 Solving -1 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3t = 0 + 1 -3t = 0 + 1 Combine like terms: 0 + 1 = 1 -3t = 1 Divide each side by '-3'. t = -0.3333333333 Simplifying t = -0.3333333333

Subproblem 2

Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4

Solution

t = {-0.3333333333, 4}

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