The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, which equation models this situation?

We must know that the are of the triangle is given by definition by
 A = (1/2) * (b) * (h)
 where 
 b = base 
 h = height 
 Substituting the values 
 A = (1/2) * (x) * (1 + 6x) 
 A = (1/2) * (x + 6x ^ 2) 
 Since the area is 13 then 
 (1/2) * (x + 6x ^ 2) = 13 
 Clearing x we have 
 6x ^ 2 + x = 26 
 6x ^ 2 + x-26 = 0 
 (x-2) * (x + 13/6) = 0 
 As we look for the base of a triangle then x> 0 
 x = 2 
 answer 
 the base is x = 2 
 6x ^ 2 + x = 26