+1431 Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2x + 8} - 7.
+129845 Multiply through by (x + 5) (2x + 8)
(x + 4)(2x + 8) = (x - 3)(x + 5) - 7(x+5)(2x + 8)
2x^2 + 16x + 32 = x^2 + 2x -15 - 7 (2x^2 + 18x + 40)
2x^2 + 16x + 32 = x^2 + 2x - 15 - 14x^2 - 126x - 280
15x^2 + 140x + 327 = 0
The solutions are
[-140 +/- sqrt [ 140^2 - 4*15*327] ] / 30 = [-140 +/- sqrt [ -20 ] ] / 30 =
[ -140 +/- 2isqrt (5) ] / 30 =
-14/3 +/- (sqrt (5) / 15) i
