735. 5) 2(x – 2)(x + 2) = (x + 1,5)² + 4(x – 5\frac{1}{16}); 6) (x – 3)(x – 2) = 7x – 1.

Решим уравнения.

1. $$2(x - 2)(x + 2) = (x + 1.5)^2 + 4(x - 5\frac{1}{16})$$
   $$2(x^2 - 4) = x^2 + 3x + 2.25 + 4x - 20\frac{1}{4}$$
   $$2x^2 - 8 = x^2 + 7x - 17.75 + 2.25$$
   $$2x^2 - x^2 - 7x - 8 + 15.5 = 0$$
   $$x^2 - 7x + 7.5 = 0$$
   $$D = b^2 - 4ac = (-7)^2 - 4 \cdot 1 \cdot 7.5 = 49 - 30 = 19$$
   $$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{7 + \sqrt{19}}{2 \cdot 1} = \frac{7 + \sqrt{19}}{2} $$
   $$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{7 - \sqrt{19}}{2 \cdot 1} = \frac{7 - \sqrt{19}}{2}$$

   Ответ: x₁ = $$\frac{7 + \sqrt{19}}{2}$$, x₂ = $$\frac{7 - \sqrt{19}}{2}$$

2. $$(x - 3)(x - 2) = 7x - 1$$
   $$x^2 - 2x - 3x + 6 = 7x - 1$$
   $$x^2 - 5x + 6 - 7x + 1 = 0$$
   $$x^2 - 12x + 7 = 0$$
   $$D = b^2 - 4ac = (-12)^2 - 4 \cdot 1 \cdot 7 = 144 - 28 = 116$$
   $$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{12 + \sqrt{116}}{2 \cdot 1} = \frac{12 + 2\sqrt{29}}{2} = 6 + \sqrt{29}$$
   $$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{12 - \sqrt{116}}{2 \cdot 1} = \frac{12 - 2\sqrt{29}}{2} = 6 - \sqrt{29}$$

   Ответ: x₁ = $$6 + \sqrt{29}$$, x₂ = $$6 - \sqrt{29}$$