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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.