Question 739864
The altitude's value is the height of the triangle.  You correctly expressed the "one side" for the triangle, which is treated as the base, since the altitude has an endpoint on this side.  


{{{(1/2)(3a-35)*a=75}}}
or
{{{(1/2)a(3a-35)=75}}}


{{{a(3a-35)=150}}}
{{{3a^2-35a=150}}}
{{{highlight(3a^2-35a-150=0)}}}, so you have done well so far.  You really want to FACTOR that trinomial?  Try if you want, but solution to quadratic formula might be more comfortable.


Using the positive square root of discriminant,
{{{a=(35+sqrt(35^2-4*3*(-150)))/(2*3)}}}
{{{a=(35+sqrt(35^2+1800))/(2*3)}}}
{{{a=(35+sqrt(3025))/(2*3)}}}
{{{a=(35+55)/(2*3)}}}
{{{a=90/6}}}
{{{highlight(a=15)}}}


FACTOR?
You could again, as I said, try to factor.  You may first try including binomial, (a-15) because one of your pairs of numbers to get 150 as a product is 15 and 10.  You would want other constant be positive number.  Best guess (educated guess) is (3a+10) and (a-15).
CHECKING THAT: {{{(3a+10)(a-15)=3a^2-45a+10a-150}}}, looks like good.