2a^2-17a+36=0

Solution for 2a^2-17a+36=0 equation:

Simplifying
2a2 + -17a + 36 = 0

Reorder the terms:
36 + -17a + 2a2 = 0

Solving
36 + -17a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + -1a)(9 + -2a) = 0

Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

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

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

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

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

Simplifying
a = 4
Subproblem 2
Set the factor '(9 + -2a)' equal to zero and attempt to solve:

Simplifying
9 + -2a = 0

Solving
9 + -2a = 0

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

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

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

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

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

Simplifying
a = 4.5
Solution
a = {4, 4.5}