24s^2=8s+10

Solution for 24s^2=8s+10 equation:

Simplifying
24s2 = 8s + 10

Reorder the terms:
24s2 = 10 + 8s

Solving
24s2 = 10 + 8s

Solving for variable 's'.

Reorder the terms:
-10 + -8s + 24s2 = 10 + 8s + -10 + -8s

Reorder the terms:
-10 + -8s + 24s2 = 10 + -10 + 8s + -8s

Combine like terms: 10 + -10 = 0
-10 + -8s + 24s2 = 0 + 8s + -8s
-10 + -8s + 24s2 = 8s + -8s

Combine like terms: 8s + -8s = 0
-10 + -8s + 24s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4s + 12s2) = 0

Factor a trinomial.
2((-1 + -2s)(5 + -6s)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -2s)' equal to zero and attempt to solve:

Simplifying
-1 + -2s = 0

Solving
-1 + -2s = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2s = 0 + 1

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

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

Divide each side by '-2'.
s = -0.5

Simplifying
s = -0.5
Subproblem 2
Set the factor '(5 + -6s)' equal to zero and attempt to solve:

Simplifying
5 + -6s = 0

Solving
5 + -6s = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6s = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6s = 0 + -5
-6s = 0 + -5

Combine like terms: 0 + -5 = -5
-6s = -5

Divide each side by '-6'.
s = 0.8333333333

Simplifying
s = 0.8333333333
Solution
s = {-0.5, 0.8333333333}