Equation: $ax^2 + bx + c=0$ Discriminant: $\Delta = b^2 - 4ac$ $\Delta \lt 0 : S=\{ \} $ $\Delta = 0 : S=\{-\frac{b}{2a} \} $ $\Delta \gt 0$ : $ S = \{\frac{-b+\sqrt \Delta}{2a} ; \frac{-b-\sqrt \Delta}{2a} \}$

Got it !

$\LARGE x^2+5x+4=0 $	$\LARGE S=\{-1;-4 \}$
$\LARGE x-x^2+42=0 $	$\LARGE S=\{7;-6 \}$
$\LARGE 3x^2-9x+6=0 $	$\LARGE 3(x^2-3x+2=0)$ and so $\LARGE x^2-3x+2=0;\;\;\;\; S=\{ 2;1 \}$
$\LARGE 2x^2+\frac{9}{16} = x $	$\LARGE 32x^2+9=16x;\;\;\;\; S=\emptyset$
$\LARGE x^2-\frac{17x}{6}=\frac{1}{2} $	$\LARGE S=\{3;-\frac{1}{6} \}$
$\LARGE \frac{x^2}{3}+\frac{12}{25}=\frac{4x}{5} $	$\LARGE S=\{\frac{6}{5} \}$
$\LARGE x^2-2ax+a^2-b^2=0 $	$\LARGE S=\{a+b;a-b \}$
$\LARGE (5x-2)(x+3)=7(x-1) $	$\LARGE S=\{-1;-\frac{1}{5} \}$