5t^2+t=120

Solution for 5t^2+t=120 equation:

Simplifying
5t2 + t = 120

Reorder the terms:
t + 5t2 = 120

Solving
t + 5t2 = 120

Solving for variable 't'.

Reorder the terms:
-120 + t + 5t2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + t + 5t2 = 0

Factor a trinomial.
(-5 + -1t)(24 + -5t) = 0

Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
Subproblem 2
Set the factor '(24 + -5t)' equal to zero and attempt to solve:

Simplifying
24 + -5t = 0

Solving
24 + -5t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-24' to each side of the equation.
24 + -24 + -5t = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -5t = 0 + -24
-5t = 0 + -24

Combine like terms: 0 + -24 = -24
-5t = -24

Divide each side by '-5'.
t = 4.8

Simplifying
t = 4.8
Solution
t = {-5, 4.8}