For this case we must solve the following quadratic equation:
[tex]2x ^ 2 -7x -15 = 0[/tex]
We must apply the following formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 2\\b = -7\\c = -15[/tex]
Substituting we have:
[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (2) (- 15)}} {2 (2)}\\x = \frac {7 \pm \sqrt {49 + 120}} {4}\\x = \frac {7 \pm \sqrt {169}} {4}\\x = \frac {7 \pm13} {4}[/tex]
Thus, the solutions are:
[tex]x_ {1} = \frac {7 + 13} {4} = \frac {20} {4} = 5\\x_ {2} = \frac {7-13} {4} = \frac {-6} {4} = - \frac {3} {2}[/tex]
ANswer:
[tex]x_ {1} = 5\\x_ {2} = - \frac {3} {2}[/tex]
