Answer:
[tex]x=1(+/-)0.5i\sqrt{10}[/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}=4x-7[/tex]
[tex]2x^{2}-4x+7=0[/tex]
so
[tex]a=2\\b=-4\\c=7[/tex]
substitute
[tex]x=\frac{4(+/-)\sqrt{(-4)^{2}-4(2)(7)}} {2(2)}[/tex]
[tex]x=\frac{4(+/-)\sqrt{-40}} {4}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
[tex]x=\frac{4(+/-)2i\sqrt{10}} {4}[/tex]
[tex]x=1(+/-)0.5i\sqrt{10}[/tex]
