Programming Challenge: a classic trigonometry problem

[Bunuel66]

Sorry to join a bit later...
There is a solution without multivariable solver and needing only a polynomial one

Let B the length of the biggest triangle (red) right edge and C the length of the left edge smaller triangle (green), with Thales (similar triangles) or a cartesian couple of equations one gets:

1) BC=15(B+C)

with Pythagore:

2) B²+x²=40²
and
3) C²+x²=30²

Then 4) B²-C²=40²-30²=700=(B-C)(B+C)

From 1)->5) B=15C/(C-15)

Using 5) in 4) gives: C⁴-30C³+700C²-21000C+157500=0 with C>15 for having B>0

A polynomial solver gives: C=25.38493804, then B=36.6659935 and x=15.98764901

Everything by hand, except solving the 4th order equation.

Regards