Question 1172699
there are several ways to factor a quadratic equation.
if all else fails, use the quadratic formula.
that formula is:
<pre>

              -b plus or minus sqrt(b^2 - 4ac)
       x =   -----------------------------------
                          2a
</pre>

the quadratic equation has to be placed in the form of:
ax^2 + bx + c = 0
a is the coefficient of the x^2 term
b is the coefficient of the x term
c is the constant.
set your equation equal to 0 and it's already in this form.
you get:
a = 3
b = 4
c = 1
solve for x to get:
x = (-4 plus sqrt(4^2 - 4*3*1)) / 6, or:
x = (-4 minus sqrt(4^2 - 4*3*1)) / 6
since sqrt(4^2 - 4*3*1) is equal to sqrt(4) which is equal to 2, you get:
x = (-4 + 2) / 6, or:
x = (-4 - 2) / 6
this gets you:
x = -1/3 or x = -1
the following graph of the equation shows that this is true.
<img src = "http://theo.x10hosting.com/2021/010803.jpg" >


for quadratic equations, the quadratic formula is the formula that will find the roots, regardless if they are real or not.


there are other ways to factor the quadratic equation as well, but the one method that works every time is the quadratic formula.


the quadratic formula only works on quadratic equations.
if you have a polynomial of a higher degree, you need to use other methods.


there are references on the web that can help you with the various ways to factor a quadratic equations.


here's a selection of some of them.
i did a search on how to solve a quadratic equaton using google.
<a href = "https://www.google.com/search?q=how+to+solve+a+quadratic+equation&rlz=1C1CHBF_en&oq=how+to+solve+a+quadratic+equation&aqs=chrome..69i57j0l7.3990j0j15&sourceid=chrome&ie=UTF-8" target = "_blank">https://www.google.com/search?q=how+to+solve+a+quadratic+equation&rlz=1C1CHBF_en&oq=how+to+solve+a+quadratic+equation&aqs=chrome..69i57j0l7.3990j0j15&sourceid=chrome&ie=UTF-8</a>