4x^2-11x+3=5x+4 How do I solve this?

4 x^2 - 16 x - 1 = 0

x = [ 16 +/- sqrt (256 + 16) ] / 8

x = [ 16 +/ - sqrt (16*17) ] / 8

x = 2 +/ - .5 sqrt 17

by the way by inspection you can see that it is going to be very close to
4 x^2 - 16 x = 0
x(x-4) = 0
x = 4 or 0

x=8 or 0

To solve the equation 4x^2 - 11x + 3 = 5x + 4, you can follow these steps:

Step 1: Combine like terms on both sides of the equation. Move all terms to one side to get a quadratic equation in standard form: 4x^2 - 11x - 5x + 3 - 4 = 0.
Simplifying further, we have: 4x^2 - 16x - 1 = 0.

Step 2: Now, we need to factorize or apply the quadratic formula to solve for x. In this case, let's use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
For our equation, a = 4, b = -16, and c = -1.

Plugging these values into the quadratic formula, we get:
x = (-(-16) ± √((-16)^2 - 4 * 4 * (-1))) / (2 * 4).

Simplifying further:
x = (16 ± √(256 + 16)) / 8
x = (16 ± √272) / 8

Step 3: Continue simplifying:
x = (16 ± 16.49) / 8
x ≈ (16 + 16.49) / 8 ≈ 32.49 / 8 ≈ 4.06
x ≈ (16 - 16.49) / 8 ≈ -0.49 / 8 ≈ -0.06

So the solutions to the equation 4x^2 - 11x + 3 = 5x + 4 are approximately x ≈ 4.06 and x ≈ -0.06.