2x-1/x-4=1+2/5x найдите корни уравнения

Найдем корень уравнения (2 * x - 1) / (x - 4) = 1 + 2 / (5 * x);

(2 * x - 1) / (x - 4) = (5 * x + 2) / (5 * x);

(x - 4) * (5 * x + 2) = (2 * x - 1) * 5 * x;

5 * x ^ 2 + 2 * x - 4 * 5 * x - 4 * 2 = 5 * x * 2 * x - 5 * x;

5 * x ^ 2 + 2 * x - 20 * x - 8 = 10 * x ^ 2 - 5 * x;

5 * x ^ 2 - 18 * x - 8 = 10 * x ^ 2 - 5 * x;

10 * x ^ 2 - 5 * x - 5 * x ^ 2 + 18 * x + 8 = 0;

5 * x ^ 2 + 13 * x + 8 = 0;

D = b ² - 4 * a * c = 13 ² - 4 · 5 · 8 = 169 - 160 = 9;

x ₁ = ( - 13 - √ 9) / (2 · 5) = ( - 13 - 3) / 10 = - 16/10 = - 1.6;

x ₂ = ( - 13 + √ 9) / (2 · 5) = ( - 13 + 3) / 10 = - 10/10 = - 1.