4a^2+5a-51=0

Solution for 4a^2+5a-51=0 equation:

Simplifying
4a2 + 5a + -51 = 0

Reorder the terms:
-51 + 5a + 4a2 = 0

Solving
-51 + 5a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-17 + -4a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-17 + -4a)' equal to zero and attempt to solve:

Simplifying
-17 + -4a = 0

Solving
-17 + -4a = 0

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

Add '17' to each side of the equation.
-17 + 17 + -4a = 0 + 17

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

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

Divide each side by '-4'.
a = -4.25

Simplifying
a = -4.25
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-4.25, 3}