4x^2=11x+3

Solution for 4x^2=11x+3 equation:

Simplifying
4x2 = 11x + 3

Reorder the terms:
4x2 = 3 + 11x

Solving
4x2 = 3 + 11x

Solving for variable 'x'.

Reorder the terms:
-3 + -11x + 4x2 = 3 + 11x + -3 + -11x

Reorder the terms:
-3 + -11x + 4x2 = 3 + -3 + 11x + -11x

Combine like terms: 3 + -3 = 0
-3 + -11x + 4x2 = 0 + 11x + -11x
-3 + -11x + 4x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-3 + -11x + 4x2 = 0

Factor a trinomial.
(-1 + -4x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.25, 3}