Question 843173
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Hi,
The hypotenuse of a right triangle is 30 feet. 
One leg is 12 less than twice the other leg {{{highlight_green(x)}}}
Good Work on the Set Up of x and (2x-12) for the legs
Applying the Pythagorean Theorem:
 x^2 + (2x-12)^2 = 30^2
 x^2 + (2x-12)(2x-12) = 30^2
 x^2 + 4x^2 + 48x + 144 = 900
   5x^2 - 48x - 756 = 0     |Form:  ax^2 + bx + c = 0
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (48+- sqrt( 17424))/(10) }}}
{{{x = (48+- 132)/(10) }}}    |Tossing out negative solution for unit measure
     x = 18ft, one leg.  The other is 24ft    {{{2*18 - 12}}}
CHECKING our answer***
 18^2 + 24^2 = 324 + 576 = 900 
Wish You the Best in your Studies.