(u^2-8u+16)/(3u^2+9u-84)

Solution for (u^2-8u+16)/(3u^2+9u-84) equation:

D( u )

3*u^2+9*u-84 = 0

3*u^2+9*u-84 = 0

3*u^2+9*u-84 = 0

3*u^2+9*u-84 = 0

DELTA = 9^2-(-84*3*4)

DELTA = 1089

DELTA > 0

u = (1089^(1/2)-9)/(2*3) or u = (-1089^(1/2)-9)/(2*3)

u = 4 or u = -7

u in (-oo:-7) U (-7:4) U (4:+oo)

(u^2-(8*u)+16)/(3*u^2+9*u-84) = 0

(u^2-8*u+16)/(3*u^2+9*u-84) = 0

u^2-8*u+16 = 0

u^2-8*u+16 = 0

DELTA = (-8)^2-(1*4*16)

DELTA = 0

u = 8/(1*2)

u = 4 or u = 4

(u-4)^2 = 0

3*u^2+9*u-84 = 0

3*(u^2+3*u-28) = 0

u^2+3*u-28 = 0

DELTA = 3^2-(-28*1*4)

DELTA = 121

DELTA > 0

u = (121^(1/2)-3)/(1*2) or u = (-121^(1/2)-3)/(1*2)

u = 4 or u = -7

3*(u+7)*(u-4) = 0

((u-4)^2)/(3*(u+7)*(u-4)) = 0

u-4 = 0 // + 4

u = 4

u in { 4} 

u belongs to the empty set