(x^2+x-6)/(3x^2+9x-30)

Solution for (x^2+x-6)/(3x^2+9x-30) equation:

D( x )

3*x^2+9*x-30 = 0

3*x^2+9*x-30 = 0

3*x^2+9*x-30 = 0

3*x^2+9*x-30 = 0

DELTA = 9^2-(-30*3*4)

DELTA = 441

DELTA > 0

x = (441^(1/2)-9)/(2*3) or x = (-441^(1/2)-9)/(2*3)

x = 2 or x = -5

x in (-oo:-5) U (-5:2) U (2:+oo)

(x^2+x-6)/(3*x^2+9*x-30) = 0

x^2+x-6 = 0

x^2+x-6 = 0

DELTA = 1^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

(x+3)*(x-2) = 0

3*x^2+9*x-30 = 0

3*(x^2+3*x-10) = 0

x^2+3*x-10 = 0

DELTA = 3^2-(-10*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-3)/(1*2) or x = (-49^(1/2)-3)/(1*2)

x = 2 or x = -5

3*(x+5)*(x-2) = 0

((x+3)*(x-2))/(3*(x+5)*(x-2)) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = -3