find the coordinates of the points of intersaction of the straight line of the staight line5x-4y+25=0 and the circle 2x^2+2y^2+7x-6Y-15=0

Step 1: Simplify the equations

The given equations are:

5x - 4y + 25 = 0 (equation of the line)

2x^2 + 2y^2 + 7x - 6y - 15 = 0 (equation of the circle)

We can simplify these equations to:

y = (5x + 25) / 4 (equation 1)

x^2 + y^2 + 7/2x - 3y - 15/2 = 0 (equation 2)

Step 2: Substitute equation 1 into equation 2

Substitute y from equation 1 into equation 2, we get:

x^2 + ((5x + 25) / 4)^2 + 7/2x - 3((5x + 25) / 4) - 15/2 = 0

Solve this equation to find the x-coordinates of the points of intersection.

Step 3: Substitute x-coordinates into equation 1

Once you have the x-coordinates, substitute them into equation 1 to find the corresponding y-coordinates.

The solutions to these equations will give you the coordinates of the points of intersection of the line and the circle.