The ages of max and his father add up to 35 years. Max's father's age is the same as five more than the square of max's age

M+f=35

f=5+m^2

sub 5+m^2 for f

m+5+m^2=35

m^2+m+5=35

minus 35 both sides

m^2+m-30=0

factor

what 2 numbers mulitply to get - 30 and add to get 1

-5 and 6

(m-5) (m+6) = 0

set to zto

m-5=0

m=5

m+6=0

m=-6

age can't be negative

max is 5

father is 30