quadratic equation 15marks

a)1) 6x^2-7x-(1/3)=2k
6x^2 - 7x - (2k + 1/3) = 0
△ = (-7)^2 - 4(6)[-(2k + 1/3)] > 0
49 + 48k + 8 > 0
48k > - 57
k > - 19/16 = - 1.1875
2) when k is the neative integer , k = - 1,the equation becomes :
6x^2 - 7x - (2(-1) + 1/3) = 0
6x^2 - 7x - 5/3 = 0
18x^2 - 21x + 5 = 0......(*)
(6x - 5)(3x - 1) = 0
x = 5/6 or x = 1/3
2b) -3(x+1)^2+7/2(x+1)-(5/6)=0
Both sides * (- 6) :
18(x+1)^2 - 21(x+1) + 5 = 0
Compare with (*) :
Here , x+1 = 5/6 or x+1 = 1/3
x = - 1 / 6 or x = - 2 / 3