With distance between points in geometry.
two equations given
y=-5/4x+3.5
4y+10.6=-5x

Rearrange equations so they look nicer:
y = -5/4x + 7/2
4y = -4x + 14

make both equations equal 4y:
4y + 10.6 = -5/x
4y = -5/x -10.6

this means that:
-4x + 14 = -5/x - 10.6

rearrange to find x:
[multiply by x]
-4x^2 +14x = -5 - 10.6x
4x^2 - 14x + 10.6x + 5 = 0
4x^2 -3.4x + 5 = 0

use the quadratic equation: x = (-b ± √(b^2 - 4*a*c)) / 2a
for this equation, a = 4, b = -3.4 and c = 5
write the answer in the form (x - answer one) (x - answer two)
this will give either two answers. Input these into the equation 4y = -4x +14 to find the coordinates.

To find the distance between these two points:

distance = √(change in x) + (change in y)