24w+5w^2-5=0

Solution for 24w+5w^2-5=0 equation:

Simplifying
24w + 5w2 + -5 = 0

Reorder the terms:
-5 + 24w + 5w2 = 0

Solving
-5 + 24w + 5w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve:

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1w = 0 + 5

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

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

Divide each side by '-1'.
w = -5

Simplifying
w = -5
Subproblem 2
Set the factor '(1 + -5w)' equal to zero and attempt to solve:

Simplifying
1 + -5w = 0

Solving
1 + -5w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5w = 0 + -1

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

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

Divide each side by '-5'.
w = 0.2

Simplifying
w = 0.2
Solution
w = {-5, 0.2}