Question

How do I solve the proportion
x+1/3 = x+5/x

Answer 1

`(x+1)/(3) = (x+5)/(x) \\ \\ 3(x+5)=x(x+1) \\ \\ 3x+15=x^2+x \\ \\ 3x+15-x^2-x=0 \\ \\ -x^2+2x+15=0 \\ \\ \boxed{\boxed{ \Delta=b^2-4ac}} \\ \\ \Delta=2^2-4\cdot(-1)\cdot15 \\ \Delta=4+60\\ \Delta=64 \\ \\ \boxed{\boxed{\text{X}_(1,2)= (-b\pm √(\Delta) )/(2a) }} \\ \\ \\ \boxed{\text{X}_(1)= (-b - √(\Delta) )/(2a) = (-2-8)/(-2) = (10)/(2) = 5} \\ \boxed{\text{X}_2= (-b+ √(\Delta) )/(2a) = (-2+8)/(-2) = (6)/(2)=3 }`