4a^2-9a+5=0

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

Simplifying
4a2 + -9a + 5 = 0

Reorder the terms:
5 + -9a + 4a2 = 0

Solving
5 + -9a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -1a)(5 + -4a) = 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 '(5 + -4a)' equal to zero and attempt to solve:

Simplifying
5 + -4a = 0

Solving
5 + -4a = 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 + -4a = 0 + -5

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

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

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

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