For this case we have the following quadratic equation:
[tex]6w ^ 2-7w-20 = 0[/tex]
Where:
[tex]a = 6\\b = -7\\c = -20[/tex]
Its roots will be given by:
[tex]w = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\w = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (6) (- 20)}} {2 (6)}\\w = \frac {7 \pm \sqrt {49 + 480}} {12}\\w = \frac {7 \pm \sqrt {529}} {12}\\w = \frac {7 \pm23} {12}[/tex]
The roots are:
[tex]w_ {1} = \frac {7 + 23} {12} = \frac {30} {12} = \frac {15} {6} = \frac {5} {2}\\w_ {2} = \frac {7-23} {12} = \frac {-16} {12} = - \frac {8} {6} = - \frac {4} {3}[/tex]
Answer:
[tex]w_ {1} = \frac {5} {2}\\w_ {2} = - \frac {4} {3}[/tex]
