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Step-by-step explanation:
First eq. is 9x^2 - 15x + 6 = 0 and second is ( 3x - 5/2 )^2 = k ⇒ ( 3x - 5/2 )^2 - k = 0.
As both are identical, both are equal.
⇒ 9x^2 - 15x + 6 = ( 3x - 5/2 )^2 - k
⇒ 9k^2 - 15x + 6 = [ 9x^2 + 25/4 - 2(5/23)x ] - k
⇒ 9k^2 - 15x + 6 = [ 9x^2 + 25/4 - 15x ] - k
⇒ 9k^2 - 15x + 6 = 9x^2 + 25/4 - 15x - k
⇒ 6 = 25/4 - k
⇒ k = 25/4 - 6
⇒ k = ( 25 - 24 ) / 4
⇒ k = 1 / 4
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