5X^2-14X-24=0

Solution for 5X^2-14X-24=0 equation:

Simplifying
5X2 + -14X + -24 = 0

Reorder the terms:
-24 + -14X + 5X2 = 0

Solving
-24 + -14X + 5X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-6 + -5X)(4 + -1X) = 0

Subproblem 1
Set the factor '(-6 + -5X)' equal to zero and attempt to solve:

Simplifying
-6 + -5X = 0

Solving
-6 + -5X = 0

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

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

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

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

Divide each side by '-5'.
X = -1.2

Simplifying
X = -1.2
Subproblem 2
Set the factor '(4 + -1X)' equal to zero and attempt to solve:

Simplifying
4 + -1X = 0

Solving
4 + -1X = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1X = 0 + -4
-1X = 0 + -4

Combine like terms: 0 + -4 = -4
-1X = -4

Divide each side by '-1'.
X = 4

Simplifying
X = 4
Solution
X = {-1.2, 4}