-1/6(x-12)+1/2(x2)=x+3

Solution for -1/6(x-12)+1/2(x2)=x+3 equation:

x in (-oo:+oo)

(-1/6)*(x-12)+(1/2)*x^2 = x+3 // - x+3

(-1/6)*(x-12)+(1/2)*x^2-x-3 = 0

(x^2)/2-1/6*(x-12)-x-3 = 0

(-1/6*2*(x-12))/2+(x^2)/2+(2*(-x))/2+(-3*2)/2 = 0

x^2-1/6*2*(x-12)+2*(-x)-3*2 = 0

x^2-1/3*x-2*x-6+4 = 0

x^2-7/3*x-6+4 = 0

x^2-7/3*x-2 = 0

x^2-7/3*x-2 = 0

x^2-7/3*x-2 = 0

DELTA = (-7/3)^2-(-2*1*4)

DELTA = 121/9

DELTA > 0

x = ((121/9)^(1/2)+7/3)/(1*2) or x = (7/3-(121/9)^(1/2))/(1*2)

x = 3 or x = -2/3

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

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

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

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

( x+2/3 )

x+2/3 = 0 // - 2/3

x = -2/3

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -2/3, 3 }