a)
2x² - 3x = 0
x(2x - 3) = 0
x = 0 ∨ 2x - 3 = 0
x = 0 ∨ 2x = 3
x = 0 ∨ x = 3/2
x = 0 ∨ x = 1,5
x ∈ {0; 1,5}
b)
[tex]3x^{2} + 7x - 20 = 0\\\\a = 3, \ b = 7, \ c = -20\\\\\Delta = b^{2}-4ac = 7^{2}-4\cdot3\cdot(-20) = 49 + 240 = 289\\\\\sqrt{\Delta} = \sqrt{289} = 17[/tex]
[tex]x_1 =\frac{-b-\sqrt{\Delta}}{2a} = \frac{-7-17}{6} = \frac{-24}{6} = -4\\\\x_2 =\frac{-b+\sqrt{\Delta}}{2a} = \frac{-7+17}{6} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3}\\\\x \in \{-4; \ 1\frac{2}{3}\}[/tex]
c)
2x(x + 3) + 5 = 3(x - 1)
2x² + 6x + 5 = 3x - 3
2x² + 6x - 3x + 5 + 3 = 0
2x² + 3x + 8 = 0
Δ = b² - 4ac = 3² - 4 · 2 · 8 = 9 - 64 = -55 < 0
Δ < 0, brak pierwiastków równania
