This problem could be done by factoring

3x² +  x - 4 = 0
 (3x+4)(x-1) = 0

3x+4= 0;  x-1=0
  3x=-4     x=1
   x=

But you are to use the quadratic formula:

3x² +  x - 4 = 0   <--- take your problem and 

3x² + 1x - 4 = 0   <--- compare it to 

ax² + bx + c = 0   <--- this 

a = 3, b = 1, c = -4 which we substitute into:   


  

 

 

 

 

That breaks into two solutions:

   and  

Simplifying the first one:

 
 
 

Simplifying the second one:

 
 
 

So the solutions are 1 and , the same
as when we solved it by factoring.  The reason we
have to use the quadratic formula is because most
quadratic equations will not factor.

Edwin