so what you do is
make into ax^2+bx+c=0 form
add-9/2 to both sides
y^2-2y+9/2=0
now we use the quadratice formula which is
x=\(\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}\)
ax^2+bx+c=0
1y^2-2y+9/2
a=1
b=-2
c=9/2
subsitute
x=\(\frac{-(-2)+/- \sqrt{(-2)^{2}-4(1)(9/2)} }{2(1)}\)
x=\(\frac{2+/- \sqrt{4-(36/2)} }{2}\)
x=\(\frac{2+/- \sqrt{4-(18)} }{2}\)
x=\(\frac{2+/- \sqrt{-14} }{2}\)
x=\(\frac{2+/- \sqrt{-14} }{2}\)
x=\(1+/- \frac{\sqrt{-14} }{2}\)
x=\(1+/- \frac{\sqrt{14} \sqrt{-1}}{2}\)
x=\(1+/- \frac{\sqrt{14} i }{2}\)
x=\(1+/- \frac{ i \sqrt{14} }{2}\)
answer is C
