в) (5x-2) / (x+2) = (6x-21) / (x-3)

в) $$ \frac{5x-2}{x+2} = \frac{6x-21}{x-3} $$

$$ (5x-2)(x-3) = (6x-21)(x+2) $$

$$ 5x^2 -15x -2x + 6 = 6x^2 + 12x -21x - 42 $$

$$ 5x^2 -17x + 6 = 6x^2 - 9x - 42 $$

$$ 6x^2 - 5x^2 - 9x + 17x - 42 - 6 = 0 $$

$$ x^2 + 8x - 48 = 0 $$

$$ D = b^2 - 4ac = 8^2 - 4 \cdot 1 \cdot (-48) = 64 + 192 = 256 $$

$$ x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-8 + \sqrt{256}}{2 \cdot 1} = \frac{-8 + 16}{2} = \frac{8}{2} = 4 $$

$$ x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-8 - \sqrt{256}}{2 \cdot 1} = \frac{-8 - 16}{2} = \frac{-24}{2} = -12 $$

Ответ: $$ x_1 = 4, x_2 = -12 $$