x^2+(2k-1)x+3k-1=0

Solution for x^2+(2k-1)x+3k-1=0 equation:

Simplifying
x2 + (2k + -1) * x + 3k + -1 = 0

Reorder the terms:
x2 + (-1 + 2k) * x + 3k + -1 = 0

Reorder the terms for easier multiplication:
x2 + x(-1 + 2k) + 3k + -1 = 0
x2 + (-1 * x + 2k * x) + 3k + -1 = 0

Reorder the terms:
x2 + (2kx + -1x) + 3k + -1 = 0
x2 + (2kx + -1x) + 3k + -1 = 0

Reorder the terms:
-1 + 3k + 2kx + -1x + x2 = 0

Solving
-1 + 3k + 2kx + -1x + x2 = 0

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 3k + 2kx + -1x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 3k + 2kx + -1x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3k + 2kx + -1x + x2 = 0 + 1
3k + 2kx + -1x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
3k + 2kx + -1x + x2 = 1

Add 'x' to each side of the equation.
3k + 2kx + -1x + x + x2 = 1 + x

Combine like terms: -1x + x = 0
3k + 2kx + 0 + x2 = 1 + x
3k + 2kx + x2 = 1 + x

Add '-1x2' to each side of the equation.
3k + 2kx + x2 + -1x2 = 1 + x + -1x2

Combine like terms: x2 + -1x2 = 0
3k + 2kx + 0 = 1 + x + -1x2
3k + 2kx = 1 + x + -1x2

Reorder the terms:
-1 + 3k + 2kx + -1x + x2 = 1 + x + -1x2 + -1 + -1x + x2

Reorder the terms:
-1 + 3k + 2kx + -1x + x2 = 1 + -1 + x + -1x + -1x2 + x2

Combine like terms: 1 + -1 = 0
-1 + 3k + 2kx + -1x + x2 = 0 + x + -1x + -1x2 + x2
-1 + 3k + 2kx + -1x + x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
-1 + 3k + 2kx + -1x + x2 = 0 + -1x2 + x2
-1 + 3k + 2kx + -1x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-1 + 3k + 2kx + -1x + x2 = 0

The solution to this equation could not be determined.