Question 1170613
the equation is x^2 = 3x - 5


subtrct 3x from both sides of the equation and add 5 to both sides of the equation to get:


x^2 - 3x + 5 = 0.


use the quadratic equation to solve this quadratic equation to get:


the roots are:


z = 1.5 + 1.6583123951777i or x = 1.5 - 1.6583123951777i


those are the roots of the equation, which are complex numbers that contain an imaginary part because the equation does not cross the line y = 0.


if the roots were real, the graph of the equation would have cross the x-axis.


the x-axis is when the value of y on the graph is equal to 0.


the quadratic equation solves for the roots, even if they are not real.


a complex number has a real part and an imaginary part.


the real part is a real number.


the imaginary part is a real number times the letter i.


the letter i represents the square root of (-1).


here's a reference on complex numbers.


<a href = "https://www.mathsisfun.com/numbers/complex-numbers.html" target = "_blank">https://www.mathsisfun.com/numbers/complex-numbers.html</a>


there are many more references on the web.
just do a search for complex numbers.