2400/(50+x)=30+x

Solution for 2400/(50+x)=30+x equation:

D( x )

x+50 = 0

x+50 = 0

x+50 = 0

x+50 = 0 // - 50

x = -50

x in (-oo:-50) U (-50:+oo)

2400/(x+50) = x+30 // - x+30

2400/(x+50)-x-30 = 0

2400/(x+50)+(-x*(x+50))/(x+50)+(-30*(x+50))/(x+50) = 0

2400-x*(x+50)-30*(x+50) = 0

2400-x^2-50*x-30*x-1500 = 0

900-x^2-80*x = 0

900-x^2-80*x = 0

900-x^2-80*x = 0

DELTA = (-80)^2-(-1*4*900)

DELTA = 10000

DELTA > 0

x = (10000^(1/2)+80)/(-1*2) or x = (80-10000^(1/2))/(-1*2)

x = -90 or x = 10

(x+90)*(x-10) = 0

((x+90)*(x-10))/(x+50) = 0

((x+90)*(x-10))/(x+50) = 0 // * x+50

(x+90)*(x-10) = 0

( x+90 )

x+90 = 0 // - 90

x = -90

( x-10 )

x-10 = 0 // + 10

x = 10

x in { -90, 10 }