5m^2=9m+2

Solution for 5m^2=9m+2 equation:

Simplifying
5m2 = 9m + 2

Reorder the terms:
5m2 = 2 + 9m

Solving
5m2 = 2 + 9m

Solving for variable 'm'.

Reorder the terms:
-2 + -9m + 5m2 = 2 + 9m + -2 + -9m

Reorder the terms:
-2 + -9m + 5m2 = 2 + -2 + 9m + -9m

Combine like terms: 2 + -2 = 0
-2 + -9m + 5m2 = 0 + 9m + -9m
-2 + -9m + 5m2 = 9m + -9m

Combine like terms: 9m + -9m = 0
-2 + -9m + 5m2 = 0

Factor a trinomial.
(-1 + -5m)(2 + -1m) = 0

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

Simplifying
-1 + -5m = 0

Solving
-1 + -5m = 0

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

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

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

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

Divide each side by '-5'.
m = -0.2

Simplifying
m = -0.2
Subproblem 2
Set the factor '(2 + -1m)' equal to zero and attempt to solve:

Simplifying
2 + -1m = 0

Solving
2 + -1m = 0

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

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

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

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

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

Simplifying
m = 2
Solution
m = {-0.2, 2}