How do u rearange 4x^2+5x+3=0 to find x?

Question

please help me

sorry i miss typed that its

4x^3+5x+3=0

Answer 1

4x³ + 5x + 3 = 0
Let x = (-1/2) :-
4(-1/8) - 5 / 2 + 3 = - 1/2 - 5/2 + 3 = 0
Thus x - (-1/2) is a factor
Use synthetic division to find other factors:-
-1/2 | 4****0*****5****3
*****|******-2****1****-3
*****| 4****-2****6****0

(x + 1/2) (4x ² - 2x + 6) = 0
2 (x + 1/2) (2x² - x + 3) = 0
(2x + 1) (2x - 3) (x + 1)

Answer 2

This is a little method that I have developed to solve cubic equations. Note: This method does NOT work every time.

4x^3+5x+3=0
or
-3=x*(4x^2+5)
from here its just a matter of finding the right pair of factors of -3. for this case x=(-1/2) works.
-3 = (-1/2)*(4*[-1/2]^2+5)=(-1/2)*(4*(1/4)+5)=(-1/2)*(1+5)=(-1/2)*6= -3.
using long division to reduce the cubic into a quadratic:
(4x^3+5x+3)/(x+(1/2)) = 4x^2-2x+6 and from the quadratic equation the other roots are: (1/4)*(1+sqrt(23)*i) and (1/4)*(1-sqrt(23)*i)