4a^2=17a+15

Solution for 4a^2=17a+15 equation:

Simplifying
4a2 = 17a + 15

Reorder the terms:
4a2 = 15 + 17a

Solving
4a2 = 15 + 17a

Solving for variable 'a'.

Reorder the terms:
-15 + -17a + 4a2 = 15 + 17a + -15 + -17a

Reorder the terms:
-15 + -17a + 4a2 = 15 + -15 + 17a + -17a

Combine like terms: 15 + -15 = 0
-15 + -17a + 4a2 = 0 + 17a + -17a
-15 + -17a + 4a2 = 17a + -17a

Combine like terms: 17a + -17a = 0
-15 + -17a + 4a2 = 0

Factor a trinomial.
(-3 + -4a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve:

Simplifying
-3 + -4a = 0

Solving
-3 + -4a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4a = 0 + 3
-4a = 0 + 3

Combine like terms: 0 + 3 = 3
-4a = 3

Divide each side by '-4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
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
Solution
a = {-0.75, 5}