5q^2+q-4=0

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

Simplifying
5q2 + q + -4 = 0

Reorder the terms:
-4 + q + 5q2 = 0

Solving
-4 + q + 5q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-1 + -1q = 0

Solving
-1 + -1q = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1q = 0 + 1
-1q = 0 + 1

Combine like terms: 0 + 1 = 1
-1q = 1

Divide each side by '-1'.
q = -1

Simplifying
q = -1
Subproblem 2
Set the factor '(4 + -5q)' equal to zero and attempt to solve:

Simplifying
4 + -5q = 0

Solving
4 + -5q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5q = 0 + -4

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

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

Divide each side by '-5'.
q = 0.8

Simplifying
q = 0.8
Solution
q = {-1, 0.8}