Help required to solve my algebra 2 homework on ages
The sum of the ages of a father and his is 45 years. Five years ago , the product of their ages was 34. What are the ages of the father and son?
x - father's age
y - son's age
x+y=45
y=45-x
(x-5)(y-5)=34
xy-5y-5x+25=34
x(45-x)-5(45-x)-5x=9
45x-x^{2}-225+5x-5x=9
-x^{2}+45x-234=0
Solving this quadratic equation, x=39 and y=45-39=6
So, father is 39 years old and son is 6 years old.