Answer:
[tex]x_1=3+2\sqrt{6}[/tex]
[tex]x_2=3-2\sqrt{6}[/tex]
Step-by-step explanation
[tex]\rule{100mm}{0.5mm}[/tex]
[tex]x^2-6x=15[/tex]
[tex]x^2-6x+\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2=15[/tex]
[tex]x^2-6x+3^2=15+3^2[/tex]
[tex]x^2-6x+9=15+9[/tex]
[tex](x-3)^2=24[/tex]
[tex]\sqrt{(x-3)^2} =\sqrt{24}[/tex]
[tex]x-3=\pm2\sqrt{6}[/tex]
[tex]\red{\boxed{x_1=3+2\sqrt{6}}}[/tex]
[tex]\red{\boxed{x_2=3-2\sqrt{6}}}[/tex]
[tex]\rule {100mm}{0.5mm}[/tex]
