4u^2-5=19u

Solution for 4u^2-5=19u equation:

Simplifying
4u2 + -5 = 19u

Reorder the terms:
-5 + 4u2 = 19u

Solving
-5 + 4u2 = 19u

Solving for variable 'u'.

Reorder the terms:
-5 + -19u + 4u2 = 19u + -19u

Combine like terms: 19u + -19u = 0
-5 + -19u + 4u2 = 0

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

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

Simplifying
-1 + -4u = 0

Solving
-1 + -4u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4u = 0 + 1
-4u = 0 + 1

Combine like terms: 0 + 1 = 1
-4u = 1

Divide each side by '-4'.
u = -0.25

Simplifying
u = -0.25
Subproblem 2
Set the factor '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5
Solution
u = {-0.25, 5}