14u^2-5u-1=0

Solution for 14u^2-5u-1=0 equation:

Simplifying
14u2 + -5u + -1 = 0

Reorder the terms:
-1 + -5u + 14u2 = 0

Solving
-1 + -5u + 14u2 = 0

Solving for variable 'u'.

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

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

Simplifying
-1 + -7u = 0

Solving
-1 + -7u = 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 + -7u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7u = 0 + 1
-7u = 0 + 1

Combine like terms: 0 + 1 = 1
-7u = 1

Divide each side by '-7'.
u = -0.1428571429

Simplifying
u = -0.1428571429
Subproblem 2
Set the factor '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 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 + -2u = 0 + -1

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

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

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {-0.1428571429, 0.5}