a) $x^2 + 5 = 3(x + 5)$

$\Leftrightarrow x^2 - 3x - 10 = 0$

$\Delta = (-3)^2 - 4\times 1\times (-10) = 49 \Rightarrow \sqrt{\Delta} = 7$

$\Rightarrow x_1 = \frac{-(-3) + 7}{2} = 5; \; x_2 = \frac{-(-3) - 7}{2} = -2$

b) $(x - 2)(x + 2) = 3x$

$\Leftrightarrow x^2 - 3x - 4 = 0$

$\Delta = (-3)^2 - 4\times 1\times (-4) = 25\Rightarrow \sqrt{\Delta} = 5$

$\Rightarrow x_1 = \frac{-(-3) + 5}{2} = 4; \; x_2 = \frac{-(-3) - 5}{2} = -1$

c) $x^2 - 3(x - 1) = 7x - 8$

$\Leftrightarrow x^2 - 10x + 11 = 0$

$\Delta = (-10)^2 - 4\times 1\times 11 = 56 \Rightarrow \sqrt{\Delta} = \sqrt{56}$

$\Rightarrow x_1 = \frac{-(-10) +\sqrt{56}}{2} = 5 + \sqrt{14}; \; x_2 = \frac{-(10) - \sqrt{56}}{2} =5 - \sqrt{14}$

d) $3(x^2 - 2x) = 6(x - 2)$

$\Leftrightarrow (x^2 - 2x) = 2(x - 2)$

$\Leftrightarrow x^2 - 4x+4 = 0$

$\Delta = (-4)^2 - 4\times 1\times 4 = 0$

$\Rightarrow x = \frac{-(-4)}{2} = 2$