a) x² - 3x - 18 = 0
Δ = b² - 4ac
Δ = (-3)² - 4 × 1 × (-18) = 9 + 72 = 81
√Δ = √81 = 9
[tex]x_{1} = \frac{3 + 9}{2*1} = \frac{12}{2} = 6[/tex]
[tex]x_{2} = \frac{3 - 9}{2*1} = \frac{-6}{2} =-3[/tex]
b) 5x - x² = x + 4
- x² + 5x - x - 4 = 0
- x² + 4x - 4 = 0
Δ = 16 - 16 = 0
[tex]x = \frac{-4}{2*(-1)} = 2[/tex]
c) (x + 3)(2x - 5) = 14x - 8
2x² - 5x + 6x -15 = 14x - 8
2x² +x - 15 - 14x + 8 = 0
2x² - 13x - 7 = 0
Δ = 169 + 56 = 225
√Δ = 15
[tex]x_{1} = \frac{13 + 15}{4} = 7\\x_{2} = \frac{13 - 15}{4} = -\frac{1}{2}[/tex]
d) 0 = - 19x + 20 - x²
x² + 19x - 20 = 0
Δ = 361 +80 = 441
√Δ = 21
[tex]x_{1} = \frac{-19 + 21}{2} = 1\\ x_{2} = \frac{-19-21}{2} = -20[/tex]
e) 3x + 2x² = 4
2x² + 3x - 4 = 0
Δ = 9 + 32 = 41
√Δ = √41
[tex]x_{1} = \frac{-3 - \sqrt{41} }{4} \\x_{2} = \frac{-3+\sqrt{41} }{4}[/tex]
