5a^2-52a+20=0

Solution for 5a^2-52a+20=0 equation:

Simplifying
5a2 + -52a + 20 = 0

Reorder the terms:
20 + -52a + 5a2 = 0

Solving
20 + -52a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -5a)(10 + -1a) = 0

Subproblem 1
Set the factor '(2 + -5a)' equal to zero and attempt to solve:

Simplifying
2 + -5a = 0

Solving
2 + -5a = 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 + -5a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5a = 0 + -2
-5a = 0 + -2

Combine like terms: 0 + -2 = -2
-5a = -2

Divide each side by '-5'.
a = 0.4

Simplifying
a = 0.4
Subproblem 2
Set the factor '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
Solution
a = {0.4, 10}