\frac{1}{2} x^{2} +3 \sqrt{7} x+7=0
a=\frac{1}{2} , b=3\sqrt7 , c=7
\Delta=b^2-4ac=(3\sqrt7)^2-4*\frac{1}{2}*7=9*7-2*7=63-14=49
\sqrt\Delta=7
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-3\sqrt7-7}{2*\frac{1}{2}}=\frac{-3\sqrt7-7}{1}=-3\sqrt7-7
x_2=\frac{-b-\sqrt\Delta}{2a}=\frac{-3\sqrt7+7}{2*\frac{1}{2}}=\frac{7-3\sqrt7}{1}=7-3\sqrt7