2a^2-7a-9=0

Solution for 2a^2-7a-9=0 equation:

Simplifying
2a2 + -7a + -9 = 0

Reorder the terms:
-9 + -7a + 2a2 = 0

Solving
-9 + -7a + 2a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
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 = {-1, 4.5}