sqrt(x+10)-sqrt(x+3)=sqrt(4x-23)

ОДЗ: x+10≥0 x+3≥0 4x-23≥0
x≥-10 x≥-3 x≥5,75
x∈[5,75; + $\infty$ )
$\sqrt{x+10}-\sqrt{x+3}=\sqrt{4x-23} \\ (\sqrt{x+10}-\sqrt{x+3})^2=(\sqrt{4x-23} )^2 \\ x+10-2\sqrt{x+10}*\sqrt{x+3}+x+3=4x-23 \\ -2\sqrt{(x+10)(x+3)}=4x-23-x-10-x-3 \\ -2\sqrt{x^2+13x+30}=2x-36 \\ \sqrt{x^2+13x+30}=18-x \\ (\sqrt{x^2+13x+30})^2=(18-x)^2 \\ x^2+13x+30=324-36x+x^2 \\ 49x=294 \\ x=294:49 \\ x=6$