For this case we must solve the following quadratic equation:
[tex]-3x ^ 2 + 1467x-86940 = 0[/tex]
If we divide both sides of the equation by 3 we have:
[tex]-x ^ 2 + 489-28980 = 0[/tex]
The solutions will come from:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = -1\\b = 489\\c = -28980[/tex]
Substituting:
[tex]x = \frac {-489 \pm \sqrt {(489) ^ 2-4 (-1) (- 28980)}} {2 (-1)}\\x = \frac {-489 \pm \sqrt {239121-115920}} {- 2}\\x = \frac {-489 \pm \sqrt {123201}} {- 2}\\x = \frac {-489 \pm351} {- 2}[/tex]
The roots are:
[tex]x_ {1} = \frac {-489 + 351} {- 2} = \frac {-138} {- 2} = 69\\x_ {2} = \frac {-489-351} {- 2} = \frac {-840} {- 2} = 420[/tex]
ANswer:
[tex]x_ {1} = 69\\x_ {2} = 420[/tex]
