24a+55=7a^2

Solution for 24a+55=7a^2 equation:

Simplifying
24a + 55 = 7a2

Reorder the terms:
55 + 24a = 7a2

Solving
55 + 24a = 7a2

Solving for variable 'a'.

Combine like terms: 7a2 + -7a2 = 0
55 + 24a + -7a2 = 0

Factor a trinomial.
(5 + -1a)(11 + 7a) = 0

Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(11 + 7a)' equal to zero and attempt to solve:

Simplifying
11 + 7a = 0

Solving
11 + 7a = 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 + 7a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7a = 0 + -11
7a = 0 + -11

Combine like terms: 0 + -11 = -11
7a = -11

Divide each side by '7'.
a = -1.571428571

Simplifying
a = -1.571428571
Solution
a = {5, -1.571428571}