Bonsoir,
x² + 5(x + 3) - 7 = 2x + 26
<=> x² + 5x + 15 - 7 = 2x + 26
<=> x² + 3x + 8 - 26 = 0
<=> x² + 3x - 18 = 0
Le discriminant est:
[tex]\Delta = 3^2 - 4 \times 1 \times (-18) = 81[/tex]
[tex]\Delta > 0[/tex], il y a deux racines simples:
[tex]x = \frac{-3 - \sqrt{81}}{2 \times 1} = \frac{-3-9}{2} = -6[/tex]
[tex]x = \frac{-3 + \sqrt{81}}{2\times 1} = \frac{-3+9}{2} = 3[/tex]
Finalement,
[tex]\boxed{x \in \{-6; 3\}}[/tex]
Bonne soirée,
Thomas
