Programming Challenge: a classic trigonometry problem

[Gil]

Yred = slope × "values on X-ax)
& slope red = opp/adj = sqrt (40² - x²) / x
Yred (at Xo, corresponding to yo = 15) <==>
sqrt (40² - x²) / x × Xo = 15
—>Xo= 15 × x/sqrt (40² - x²) (eq 1)

Green (at Xo):
Intercept + slope × Xo = 15 (eq 2)
& slope Red =- sqrt (30²-x²) / x
& intercept = sqrt (30²-x²)

EQ 2 Green (at Xo): <==>

sqrt (30²-x²) - [sqrt (30²-x²) / x] × Xo = 15
sqrt (30²-x²) - [sqrt (30²-x²) / x] × x/sqrt (40² - x²) = 15 (with eq 1)

Solve, getting rid of sqrt and writing x² = X

And we find:
'X^4.+-4100.*X^3.+5755000.*X^2.+-3091500000.*X+478406250000.'

Then:
[ 1. -4100. 5755000. -3091500000. 478406250000. ] in HP50G polynomial solver:

—>Roots:
[ (255.604920821,0.) (804.095455958,0.) (1520.14981161,129.64234902) (1520.14981161,-129.64234902) ]

Question :
Is sqrt of 804.095455958 not an acceptable solution?