x^2=4x-5
subtract 4x from both sides
x^2-4x=-5
add 5 to both sides
x^2-4x+5=0
input into quadratic formula which is x=[tex] \frac{-b+ \sqrt{b^2-4ac} }{2a} [/tex] or [tex] \frac{-b- \sqrt{b^2-4ac} }{2a} [/tex]
si ax^2+bx+c
so a=1
b=-4
c=5
input
[tex] \frac{-(-4)+ \sqrt{-4^2-4(1)(5)} }{2(1)} [/tex]=[tex] \frac{4+ \sqrt{16-20} }{2(1)} [/tex]=[tex] \frac{4+ \sqrt{-4} }{2} [/tex]=[tex] \frac{4+ \sqrt{4} times \sqrt{-1} }{2} [/tex] [tex] \frac{4+2 times \sqrt{-1} }{2}= \frac{6 times \sqrt{-1} }{2}=3 times \sqrt{-1} [\tex][\tex]\sqrt{-1} [/tex] representeds by 'i' so solution is 3i
then if other way around then wyou would do
[tex] \frac{-(-4)- \sqrt{-4^2-4(1)(5)} }{2(1)} [/tex]=[tex] \frac{4- \sqrt{16-20} }{2(1)}= \frac{4- \sqrt{-4} }{2} =\frac{4- \sqrt{4} times \sqrt{-1} }{2}= \frac{4-2 times \sqrt{-1} }{2}=\frac{2 \sqrt{-1} }{2}= \sqrt{-1} [/tex] and [\tex]\sqrt{-1} [/tex] is represented by i
the solution is x=3i or i (i=[tex] \sqrt{-1} [/tex])
but i is not real, it is imaginary so there are no real solution so the answer is C
