Answer:
[tex]$x_{1}=\frac{3}{2}+\frac{i}{2}\\$[/tex]
[tex]$x_{2}=\frac{3}{2}-\frac{i}{2}$[/tex]
Step-by-step explanation:
It is a Quadratic Equation
[tex]2x^2-6x+5=0[/tex]
Once it cannot be easily factored, you solve it using the quadratic formula or completing the square. I will use the quadratic formula.
[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]
[tex]$x=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot 2\cdot 5}}{2\cdot 2}$[/tex]
The discriminant is negative, therefore we got complex solutions.
[tex]\Delta= \sqrt{-4}= \sqrt{4i} =2i[/tex]
[tex]$x=\frac{6\pm 2i}{4}$[/tex]
[tex]$x_{1}=\frac{3+i}{2} $[/tex]
[tex]$x_{2}=\frac{3-i}{2} $[/tex]
Now, just rewrite the roots in standard complex form
[tex]$x_{1}=\frac{3}{2}+\frac{i}{2}\\$[/tex]
[tex]$x_{2}=\frac{3}{2}-\frac{i}{2}$[/tex]
