8u^2-78u+19=0

Solution for 8u^2-78u+19=0 equation:

Simplifying
8u2 + -78u + 19 = 0

Reorder the terms:
19 + -78u + 8u2 = 0

Solving
19 + -78u + 8u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(1 + -4u)(19 + -2u) = 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 '(19 + -2u)' equal to zero and attempt to solve:

Simplifying
19 + -2u = 0

Solving
19 + -2u = 0

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

Add '-19' to each side of the equation.
19 + -19 + -2u = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2u = 0 + -19
-2u = 0 + -19

Combine like terms: 0 + -19 = -19
-2u = -19

Divide each side by '-2'.
u = 9.5

Simplifying
u = 9.5
Solution
u = {0.25, 9.5}