Question

Find all complex solutions of 5x^2-6x+2=0.

Answer 1

We use quadratic formula for that one
remember that √-1=i

so

for
ax^2+bx+c=0
$x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}$
so
given
5x^2-6x+2=0
a=5
b=-6
c=2

$x=\frac{-(-6)+/-\sqrt{(-6)^2-4(5)(2)}}{2(5)}$
$x=\frac{6+/-\sqrt{36-40}}{10}$
$x=\frac{6+/-\sqrt{-4}}{10}$
$x=\frac{6+/-2i}{10}$

$x=\frac{3}{5}+\frac{i}{5}, \frac{3}{5}-\frac{i}{5}$