[latex] \sqrt{6-10x}=5+x[/latex] решите уравнение

[latex]\sqrt{6 - 10x} = 5 + x\\\\ \ 5 + x \geq 0, \ x \geq -5; \ 6 - 10x \geq 0, \ -10x \geq -6, \ x \leq \frac{3}{5} \\\\ 6 - 10x = 25 + 10x + x^2\\\\ x^2 + 20x + 19 = 0\\\\ x^2 + 19x + x + 19 = 0\\\\ x(x + 19) + (x+19) = 0\\\\ (x + 1)(x+19) = 0\\\\ x_1 = -1, \ x_2 = -19 < -5\\\\ \boxed{x = -1}[/latex]