84x^2-5=x

Solution for 84x^2-5=x equation:

Simplifying
84x2 + -5 = x

Reorder the terms:
-5 + 84x2 = x

Solving
-5 + 84x2 = x

Solving for variable 'x'.

Reorder the terms:
-5 + -1x + 84x2 = x + -1x

Combine like terms: x + -1x = 0
-5 + -1x + 84x2 = 0

Factor a trinomial.
(-5 + -21x)(1 + -4x) = 0

Subproblem 1
Set the factor '(-5 + -21x)' equal to zero and attempt to solve:

Simplifying
-5 + -21x = 0

Solving
-5 + -21x = 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 + -21x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -21x = 0 + 5
-21x = 0 + 5

Combine like terms: 0 + 5 = 5
-21x = 5

Divide each side by '-21'.
x = -0.2380952381

Simplifying
x = -0.2380952381
Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-0.2380952381, 0.25}