4q^2-9q+5=0

Solution for 4q^2-9q+5=0 equation:

Simplifying
4q2 + -9q + 5 = 0

Reorder the terms:
5 + -9q + 4q2 = 0

Solving
5 + -9q + 4q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + -1q)(5 + -4q) = 0

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

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

Simplifying
q = 1
Subproblem 2
Set the factor '(5 + -4q)' equal to zero and attempt to solve:

Simplifying
5 + -4q = 0

Solving
5 + -4q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4q = 0 + -5
-4q = 0 + -5

Combine like terms: 0 + -5 = -5
-4q = -5

Divide each side by '-4'.
q = 1.25

Simplifying
q = 1.25
Solution
q = {1, 1.25}