5t^2-t-22=0

Solution for 5t^2-t-22=0 equation:

Simplifying
5t2 + -1t + -22 = 0

Reorder the terms:
-22 + -1t + 5t2 = 0

Solving
-22 + -1t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-2 + -1t)(11 + -5t) = 0

Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve:

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(11 + -5t)' equal to zero and attempt to solve:

Simplifying
11 + -5t = 0

Solving
11 + -5t = 0

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

Add '-11' to each side of the equation.
11 + -11 + -5t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5t = 0 + -11
-5t = 0 + -11

Combine like terms: 0 + -11 = -11
-5t = -11

Divide each side by '-5'.
t = 2.2

Simplifying
t = 2.2
Solution
t = {-2, 2.2}