Algebra

Find all possible values of a, if the equations ax^2+5x+1=4x^2+7x-4 has two different real roots

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$ax^2+5x+1=4x^2+7x-4\\ ax^2-4x^2+5x-7x+1+4=0\\ (a-4)x^2-2x+5=0$

$a\in\mathbb R\ |$  $-\infty$  $<$  $a$  $<\ 4.2$  $and$ $\ a\neq 4$

With $a\in\{4,4.2\}$, the equations have only one real root.

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