(x^2-x)/5-(7-x^2)/6=7

Solution for (x^2-x)/5-(7-x^2)/6=7 equation:

x in (-oo:+oo)

(x^2-x)/5-((7-x^2)/6) = 7 // - 7

(x^2-x)/5-((7-x^2)/6)-7 = 0

(x^2-x)/5+(-1*(7-x^2))/6-7 = 0

(6*(x^2-x))/(5*6)+(-1*5*(7-x^2))/(5*6)+(-7*5*6)/(5*6) = 0

6*(x^2-x)-1*5*(7-x^2)-7*5*6 = 0

11*x^2-6*x-210-35 = 0

11*x^2-6*x-245 = 0

11*x^2-6*x-245 = 0

11*x^2-6*x-245 = 0

DELTA = (-6)^2-(-245*4*11)

DELTA = 10816

DELTA > 0

x = (10816^(1/2)+6)/(2*11) or x = (6-10816^(1/2))/(2*11)

x = 5 or x = -49/11

(x+49/11)*(x-5) = 0

((x+49/11)*(x-5))/(5*6) = 0

((x+49/11)*(x-5))/(5*6) = 0 // * 5*6

(x+49/11)*(x-5) = 0

( x+49/11 )

x+49/11 = 0 // - 49/11

x = -49/11

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -49/11, 5 }