Question

What is -3×^2+1467x-86940=0 ?​

Answer 1

For this case we must solve the following quadratic equation:

$-3x ^ 2 + 1467x-86940 = 0$

If we divide both sides of the equation by 3 we have:

$-x ^ 2 + 489-28980 = 0$

The solutions will come from:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Where:

$a = -1\\b = 489\\c = -28980$

Substituting:

$x = \frac {-489 \pm \sqrt {(489) ^ 2-4 (-1) (- 28980)}} {2 (-1)}\\x = \frac {-489 \pm \sqrt {239121-115920}} {- 2}\\x = \frac {-489 \pm \sqrt {123201}} {- 2}\\x = \frac {-489 \pm351} {- 2}$

The roots are:

$x_ {1} = \frac {-489 + 351} {- 2} = \frac {-138} {- 2} = 69\\x_ {2} = \frac {-489-351} {- 2} = \frac {-840} {- 2} = 420$

ANswer:

$x_ {1} = 69\\x_ {2} = 420$