Solve √2 $x^2+7x+5$√2 = 0 using the quadratic formula.

Here $a=\sqrt{2},b=7,c=5\sqrt{2}$, so $4ac=4\times \sqrt{2}\times 5\sqrt{2}=40$ and $D=49-40=9.x=\frac{-7\pm 3}{2\sqrt{2}}$, giving $\frac{-4}{2\sqrt{2}}=-\sqrt{2}$ and $\frac{-10}{2\sqrt{2}}=-\frac{5\sqrt{2}}{2}$. Both roots are negative because $b$ and $c$ are both positive. Treating $\sqrt{2}\times 5\sqrt{2}$ as $5\sqrt{2}$ makes $D$ look negative and suggests "no real roots".