x^2/6-x/2=3(x-5)

Solution for x^2/6-x/2=3(x-5) equation:

x in (-oo:+oo)

(x^2)/6-(x/2) = 3*(x-5) // - 3*(x-5)

(x^2)/6-(3*(x-5))-(x/2) = 0

(x^2)/6-3*(x-5)-(x/2) = 0

(x^2)/6-3*(x-5)-x/2 = 0

(-3*2*6*(x-5))/(2*6)+(2*x^2)/(2*6)+(6*(-x))/(2*6) = 0

2*x^2-3*2*6*(x-5)+6*(-x) = 0

2*x^2-36*x-6*x+180 = 0

2*x^2-42*x+180 = 0

2*x^2-42*x+180 = 0

2*(x^2-21*x+90) = 0

x^2-21*x+90 = 0

DELTA = (-21)^2-(1*4*90)

DELTA = 81

DELTA > 0

x = (81^(1/2)+21)/(1*2) or x = (21-81^(1/2))/(1*2)

x = 15 or x = 6

2*(x-6)*(x-15) = 0

(2*(x-6)*(x-15))/(2*6) = 0

(2*(x-6)*(x-15))/(2*6) = 0 // * 2*6

2*(x-6)*(x-15) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-15 )

x-15 = 0 // + 15

x = 15

( x-6 )

x-6 = 0 // + 6

x = 6

x in { 15, 6 }