4x^2-19x=5

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Solution for 4x^2-19x=5 equation:


Simplifying
4x2 + -19x = 5

Reorder the terms:
-19x + 4x2 = 5

Solving
-19x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -19x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -19x + 4x2 = 0

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

Subproblem 1

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

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 = {-0.25, 5}

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