5a^2-3a-14=0

Solution for 5a^2-3a-14=0 equation:

Simplifying
5a2 + -3a + -14 = 0

Reorder the terms:
-14 + -3a + 5a2 = 0

Solving
-14 + -3a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -5a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -5a)' equal to zero and attempt to solve:

Simplifying
-7 + -5a = 0

Solving
-7 + -5a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5a = 0 + 7
-5a = 0 + 7

Combine like terms: 0 + 7 = 7
-5a = 7

Divide each side by '-5'.
a = -1.4

Simplifying
a = -1.4
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-1.4, 2}