3x^2-4x-1=54

Solution for 3x^2-4x-1=54 equation:

Simplifying
3x2 + -4x + -1 = 54

Reorder the terms:
-1 + -4x + 3x2 = 54

Solving
-1 + -4x + 3x2 = 54

Solving for variable 'x'.

Reorder the terms:
-1 + -54 + -4x + 3x2 = 54 + -54

Combine like terms: -1 + -54 = -55
-55 + -4x + 3x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-55 + -4x + 3x2 = 0

Factor a trinomial.
(-11 + -3x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

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

Simplifying
x = 5
Solution
x = {-3.666666667, 5}