Solve the equation: | 3x^2 – 9x + 4| = 14

l 3x^2 - 9x +4 l = 14

We have
two cases:

Case(1);

3x^2 - 9x
+ 4 = 14

==> 3x^2 - 9x +4 -14 =
0

==> 3x^2 - 9x -10 =
0

Now we will use the quadratic equation to solve for
x.

==> x1 = ( 9 + sqrt(81+4*3*10) /
6

             = ( 9 + sqrt(201) /
6

  ==> x1= ( 3/2) + sqrt(210) /
6

==> x2= (3/2) -
sqrt(210) /
6

 

Case(2).

==>
-(3x^2 -9x +4 ) = 14

==> -3x^2 + 9x -4 =
14

==> -3x^2 + 9x -18 =
0

==> x1= ( -9 + sqrt(81-4*3*18) /
-6

            = ( -9 + sqrt(135)*i ) /
-6

              = ( 3/2) + 3sqrt(15) i
/6

             = (3/2) + (sqrt15 /2
)*i

==> x1= (3/2) + (sqrt15 / 2)
*i

==> x2 = (3/2) -
9sqrt15 /2)*i