2a^2+7a-22=0

Solution for 2a^2+7a-22=0 equation:

Simplifying
2a2 + 7a + -22 = 0

Reorder the terms:
-22 + 7a + 2a2 = 0

Solving
-22 + 7a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-11 + -2a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-11 + -2a)' equal to zero and attempt to solve:

Simplifying
-11 + -2a = 0

Solving
-11 + -2a = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2a = 0 + 11
-2a = 0 + 11

Combine like terms: 0 + 11 = 11
-2a = 11

Divide each side by '-2'.
a = -5.5

Simplifying
a = -5.5
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

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

Simplifying
a = 2
Solution
a = {-5.5, 2}