This time, I have been trying to find the equation of intersection point between line and ellipse. I wrote an equation but the delta is negative so I can`t find the roots.

x,y is the intersection point,
x1, y1 is the start point of the line
h, k is the center point of the line
a is the major radius of the ellipse lies on X axis
b is the minor radius of the ellipse lies on Y axis

m = tan(AngleOfLine)

(y - y1) = m * (x - x1) -> y = m * (x - x1) + y1

I put m * (x - x1) + y1 instead of y in the ellipse equation
(x - h) ^ 2 / a ^ 2 + (y- k) ^ 2 / b ^ 2 = 1

and tried to solve.
After I opened all of the paranthesises (very long line) and converted the equation in ax^2 + bx + c = 0 form, but the delta is negative.

Even I tried to resolve this equation, the result is the same. I`m not sure if I`m doing something wrong but it seems right.

Would you please help me to find that intersection point?
Thanks in advance.