For which values of k will the roots of the equation
x^2 = 2x(3k + 1) - 7(2k + 3) be equal?
x^2 = 6xk + 2 - 14k - 21
x^2 = 6xk - 14k -19
Is this a new start?
$x^2=2x(3k+1)-7(2k+3)$
$x^2=6kx+2x-14k-21$
$x^2=(6k+2)x-(14k+21)$
$x^2-(6k+2)x+(14k+21)=0$
For roots to be equal
$b^2-4ac=0$
$[-(6k+2)]^2-4×1×(14k+21)=0$
$36k^2+4+24k-56k-84=0$
$36k^2-32k-80=0$
$4(9k^2-8k-20)=0$
$9k^2-8k-20=0$
$(k-2)(9k+10)=0$
$k=2,\;-\dfrac{10}{9}$