21+x - 28-3x=121+x под корнем и 28-3x под корнем

ОДЗ 21+x≥0 28-3x≥0
x≥-21 3x≤28
x≤7
x∈[-21; 7]

$\sqrt{21+x}-\sqrt{28-3x}=1 \\ (\sqrt{21+x}-\sqrt{28-3x})^2=1^2 \\ 21+x-2*\sqrt{21+x}*\sqrt{28-3x}+28-3x=1 \\ 49-2x-2*\sqrt{588-35x-3x^2}=1 \\ 2*\sqrt{588-35x-3x^2}=48-2x \\ \sqrt{588-35x-3x^2}=24-x \\ ( \sqrt{588-35x-3x^2})^2=(24-x)^2 \\ 588-35x-3x^2=576-48x+x^2 \\ 4x^2-13x-12=0 \\ D=169+192=361 \\ x_1=\frac{13-19}{8}=-\frac{3}{4}=-0,75 \ \ \ \ \ \ \ \ \ x_2=\frac{13+19}{8}=4$