Question

Quadratic Equation.
13x(to the power 2)-118x+240=0

Answer 1

     Solving    13x2-118x+240 = 0 by the Quadratic Formula .

 According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and C  are numbers, often called coefficients, is given by :
                                     
            - B  ±  √ B2-4AC
  x =   ————————
                      2A 

  In our case,  A   =     13
                      B   =   -118
                      C   =  240 

Accordingly,  B2  -  4AC   =
                     13924 - 12480 =
                     1444

Applying the quadratic formula :

               118 ± √ 1444 
   x  =    ———————
                        26

Can  √ 1444 be simplified ?

Yes!   The prime factorization of  1444   is
   2•2•19•19  
To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. secondroot).

√ 1444   =  √ 2•2•19•19   =2•19•√ 1   =
                ±  38 • √ 1   =
                ±  38 

So now we are looking at:
           x  =  ( 118 ± 38) / 26

Two real solutions:

x =(118+√1444)/26=(59+19)/13= 6.000 

or:

x =(118-√1444)/26=(59-19)/13= 3.077 

Answer 2

13x^2-118x+240 = 0
Splitting the middle term
13x^2 - 78x - 40x +240 = 0
13x(x - 6) -40(x - 6) = 0
(13x-40) (x-6) = 0
13x-40 = 0
x = 40/13
x-6 = 0
x = 6

Brainelist it if it helps