5X^2-4X=1

Solution for 5X^2-4X=1 equation:

Simplifying
5X2 + -4X = 1

Reorder the terms:
-4X + 5X2 = 1

Solving
-4X + 5X2 = 1

Solving for variable 'X'.

Reorder the terms:
-1 + -4X + 5X2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -4X + 5X2 = 0

Factor a trinomial.
(-1 + -5X)(1 + -1X) = 0

Subproblem 1
Set the factor '(-1 + -5X)' equal to zero and attempt to solve:

Simplifying
-1 + -5X = 0

Solving
-1 + -5X = 0

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

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

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

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

Divide each side by '-5'.
X = -0.2

Simplifying
X = -0.2
Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {-0.2, 1}