24x^2=x+3

Solution for 24x^2=x+3 equation:

Simplifying
24x2 = x + 3

Reorder the terms:
24x2 = 3 + x

Solving
24x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-3 + -1x + 24x2 = 3 + x + -3 + -1x

Reorder the terms:
-3 + -1x + 24x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-3 + -1x + 24x2 = 0 + x + -1x
-3 + -1x + 24x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + -1x + 24x2 = 0

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

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

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

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

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

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

Simplifying
x = -0.3333333333
Subproblem 2
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x = 0 + -3
-8x = 0 + -3

Combine like terms: 0 + -3 = -3
-8x = -3

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Solution
x = {-0.3333333333, 0.375}