Guten Tag,

Hallo Timo!

$\sqrt{x+13}=\sqrt{2x+12}-1$                     [quadrieren

$x+13=2x+12-2\sqrt{2x+12}+1$  [Wurzel nach links

$2\sqrt{2x+12}=2x+12+1-x-13$  [ addieren

$2\sqrt{2x+12}=x$                                       [quadrieren 

$4(2x+12)=x^2$                        [multiplizieren

$8x+48=x^2$                             [alles n. links

$x^2-8x-48=0$                      [p/q zuordnen

         p          q

$x=-\frac{p}{2}\pm\sqrt{(\frac{p}{2})^2-q}$              [p/q-Formel

$x=\frac{8}{2}\pm\sqrt{(\frac{8}{2})^2+48}$               [p/q einsetzen    

$x=4\pm\sqrt{16+48}$                    [ausrechnen

$x=4\pm\sqrt{64}$                              [      "

$x=4\pm8$                                    [      "

$x_1=12\\ x_2=-4$ 

Gruß   !