請幫手數學問題!!!!!

題目的意思是：
一元二次方程 12x² - 16kx + 5k² = 0，其中 k 為整數。已知 3/2 為方程式其中一根（即 x 可以是 3/2）。使用一元二次方程的公式，計算
a) k 之值。

解法是首先解一元二次方程 (quadratic equation) :
12x² - 16kx + 5k² = 0
得 x = 5k/6 or x = k/2

方程式的兩根 (two roots)是5k/6 和k/2，但題目已知其中一根 (one root) 等於 3/2。
即5k/6 = 3/2 或k/2 = 3/2

1) 若root 5k/6 = 3/2，則
5k/6 = 3/2
k = 9/5 (rejected) ...... 因 k 為整數 (integer)

2) 若root k/2 = 3/2，則
k/2 = 3/2
k = 3


我的解法：
3/2 is a roots of the equation.
Hence, put x = 3/2 into the equation :
12x² - 16kx + 5k² = 0
12(3/2)² - 16k(3/2) + 5k² = 0
5k² - 24k + 27 = 0
(k - 3)(5k - 9) = 0
k = 3 or k = 9/5 (rejected forkshould be an integer)

a)12x^2－16kx+5k^2=0 is a quadratic equation in x where k is an interger.Itis
given that 3/2 is a root of the equation.By using the quadratic formula，find
a)the value of k
Sol
12x^2－16kx+5k^2=0
x=｛16k+/-√[(16k)^2－4*12*5k^2]｝/24
=[16k+/-4k]/24
x=5k/6 or x=k/2
(1) 5k/6=3/2
k=(3/2)*(6/5)=18/10=9/5 (reject) k is an interger
(2) k/2=3/2
k=3
b)the other root of the equation
Sol
12x^2－48x+45=0
4x^2－16x+15=0
(2x－5)(2x－3)=0
x=5/2 or x=3/2
the other root of the equation=5/2