4x^2=-x+5

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

Simplifying
4x2 = -1x + 5

Reorder the terms:
4x2 = 5 + -1x

Solving
4x2 = 5 + -1x

Solving for variable 'x'.

Reorder the terms:
-5 + x + 4x2 = 5 + -1x + -5 + x

Reorder the terms:
-5 + x + 4x2 = 5 + -5 + -1x + x

Combine like terms: 5 + -5 = 0
-5 + x + 4x2 = 0 + -1x + x
-5 + x + 4x2 = -1x + x

Combine like terms: -1x + x = 0
-5 + x + 4x2 = 0

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

Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 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 + -4x = 0 + 5

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

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

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25
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 = {-1.25, 1}