remember, √-1=i
also
for ax²+bx+c=0
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so
given
3x²+3x+4=0
a=3
b=3
c=4
[tex]x=\frac{-3+/-\sqrt{3^2-4(3)(4)}}{2(3)}[/tex]
[tex]x=\frac{-3+/-\sqrt{9-48}}{6}[/tex]
[tex]x=\frac{-3+/-\sqrt{-39}}{6}[/tex]
[tex]x=\frac{-3+/-(\sqrt{-1})(\sqrt{39})}{6}[/tex]
[tex]x=\frac{-3+/-(i)(\sqrt{39})}{6}[/tex]
[tex]x=\frac{-3+/-i\sqrt{39}}{6}[/tex]
the solutions (in a+bi form) are
[tex]x=\frac{-1}{2}+\frac{i\sqrt{39}}{6}, \frac{-1}{2}-\frac{i\sqrt{39}}{6}[/tex]
