Answer:
Option C. [tex]x=\frac{1(+/-)\sqrt{19}} {2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]2x^{2} -2x-9=0[/tex]
so
[tex]a=2\\b=-2\\c=-9[/tex]
substitute in the formula
[tex]x=\frac{2(+/-)\sqrt{-2^{2}-4(2)(-9)}} {2(2)}[/tex]
[tex]x=\frac{2(+/-)\sqrt{76}} {4}[/tex]
[tex]x=\frac{2(+/-)2\sqrt{19}} {4}[/tex]
[tex]x=\frac{1(+/-)\sqrt{19}} {2}[/tex]
