Math question - word problem...possibly polynomial?

Question

There's a 6 ft wall. Support beam is 1 foot less than 3 times the length of the ground. The support beam goes from the top of the wall to the ground. What is the length of the beam? I got 30 ft... is this correct? I came up with the equation 3x(3x-1) = 6 and then converted that to 9x^2 - 3x - 6 and then worked from there....Did I do this wrong?

Answer 1

Okay, letting h be length of support beam, and x be length of ground, then h=3x-1, and 6^2+x^2=h^2.
So, 36+x^2=(3x-1)^2 =9x^2-6x+1.
So, 8x^2-6x-35=0.
And solving I get x=-7/4 and 5/2.
So, of course -7/4 wouldn't make sence, so x=5/2=2.5.
So the support beam 3x-1 = (3*2.5)-1=6.5 foot.