2x^2-5x+6=24

Solution for 2x^2-5x+6=24 equation:

Simplifying
2x2 + -5x + 6 = 24

Reorder the terms:
6 + -5x + 2x2 = 24

Solving
6 + -5x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
6 + -24 + -5x + 2x2 = 24 + -24

Combine like terms: 6 + -24 = -18
-18 + -5x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-18 + -5x + 2x2 = 0

Factor a trinomial.
(-2 + -1x)(9 + -2x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-2, 4.5}