24u^2-5u-1=0

Solution for 24u^2-5u-1=0 equation:

Simplifying
24u2 + -5u + -1 = 0

Reorder the terms:
-1 + -5u + 24u2 = 0

Solving
-1 + -5u + 24u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -8u)(1 + -3u) = 0

Subproblem 1
Set the factor '(-1 + -8u)' equal to zero and attempt to solve:

Simplifying
-1 + -8u = 0

Solving
-1 + -8u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -8u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8u = 0 + 1
-8u = 0 + 1

Combine like terms: 0 + 1 = 1
-8u = 1

Divide each side by '-8'.
u = -0.125

Simplifying
u = -0.125
Subproblem 2
Set the factor '(1 + -3u)' equal to zero and attempt to solve:

Simplifying
1 + -3u = 0

Solving
1 + -3u = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3u = 0 + -1
-3u = 0 + -1

Combine like terms: 0 + -1 = -1
-3u = -1

Divide each side by '-3'.
u = 0.3333333333

Simplifying
u = 0.3333333333
Solution
u = {-0.125, 0.3333333333}