Can we show $(b^2 - 2ac)x^2 + 4(a + c)x = 8$ always has real roots?
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Ref: R8812

Question

Prove that the roots of $(b^2 - 2ac)x^2 + 4(a + c)x = 8$ are real if $a$, $b$, $c$ are real. Find the conditions that the roots are equal.