$a)$

$2 x^{2} - 3 = 6 - x^{2} ∣ - 6 + x^{2}$

$3 x^{2} - 9 = 0 ∣ : 3$

$x^{2} - 3 = 0$

$(x - 3) (x + 3) = 0$

$x - 3 = 0 lub x + 3 = 0$

$x = 3 lub x = - 3$

$b)$

$(\frac{1}{3} x + 1)^{2} = 4$

$\frac{1}{9} x^{2} + \frac{2}{3} x + 1 = 4$

$\frac{1}{9} x^{2} + \frac{2}{3} x - 3 = 0 ∣ \cdot 9$

$x^{2} + 6 x - 27 = 0$

$Δ = 6^{2} - 4 \cdot 1 \cdot (- 27) = 36 + 108 = 144$

$x_{1} = \frac{- 6 - 12}{2} = \frac{- 18}{2} = - 9$

$x_{2} = \frac{- 6 + 12}{2} = \frac{6}{2} = 3$

$c)$

$(3 x - 2)^{2} = (x + 1)^{2}$

$9 x^{2} - 12 x + 4 = x^{2} + 2 x + 1 ∣ - x^{2} - 2 x - 1$

$8 x^{2} - 14 x + 3 = 0$

$Δ = (- 14)^{2} - 4 \cdot 8 \cdot 3 = 196 - 96 = 100$

$x_{1} = \frac{14 - 10}{2 \cdot 8} = \frac{4}{16} = \frac{1}{4}$

$x_{2} = \frac{14 + 10}{2 \cdot 8} = \frac{24}{16} = \frac{6}{4} = \frac{3}{2}$

$d)$

$(2 x - 4) (2 x + 3) = 1 - 11 x$

$4 x^{2} + 6 x - 8 x - 12 = 1 - 11 x ∣ - 1 + 11 x$

$4 x^{2} + 9 x - 13 = 0$

$Δ = 9^{2} - 4 \cdot 4 \cdot (- 13) = 81 + 208 = 289$

$x_{1} = \frac{- 9 - 17}{2 \cdot 4} = \frac{- 26}{8} = - \frac{13}{4}$

$x_{2} = \frac{- 9 + 17}{2 \cdot 4} = \frac{8}{8} = 1$

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