Which are the solutions of the quadratic equation?x2=7X+4-7-165 -7 + 165-7.07- 165 7+ / 657,0

For this case we must find the roots of the following equation:[tex]x ^ 2-7x-4 = 0[/tex]We have to:[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]Where:[tex]a = 1\\b = -7\\c = -4[/tex]Substituting the values:[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 16}} {2}\\x = \frac {7\pm\sqrt {65}} {2}[/tex]We have two roots:[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]Answer:[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]