735.1) 2x2 + x − 3 = 0; 3) 2x²-9x = 35;

Решим уравнения.

1. $$2x^2 + x - 3 = 0$$
   $$D = b^2 - 4ac = 1^2 - 4 \cdot 2 \cdot (-3) = 1 + 24 = 25$$
   $$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-1 + \sqrt{25}}{2 \cdot 2} = \frac{-1 + 5}{4} = \frac{4}{4} = 1$$
   $$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-1 - \sqrt{25}}{2 \cdot 2} = \frac{-1 - 5}{4} = \frac{-6}{4} = -1.5$$

   Ответ: x₁ = 1, x₂ = -1.5

2. $$2x^2 - 9x = 35$$
   $$2x^2 - 9x - 35 = 0$$
   $$D = b^2 - 4ac = (-9)^2 - 4 \cdot 2 \cdot (-35) = 81 + 280 = 361$$
   $$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{9 + \sqrt{361}}{2 \cdot 2} = \frac{9 + 19}{4} = \frac{28}{4} = 7$$
   $$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{9 - \sqrt{361}}{2 \cdot 2} = \frac{9 - 19}{4} = \frac{-10}{4} = -2.5$$

   Ответ: x₁ = 7, x₂ = -2.5