You start with f(x)=x^2+8x+10. First you have to establish its degree, which is 2 because the highest exponent is 2. That being said, you can apply the quadratic formula, namely:
ax^2+bx+c=0\implies x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
In this particular case, a is 1, b is 8 and c is 10, and therefore:
x=\frac{-8\pm\sqrt{8^2-4\cdot 1\cdot 10}}{2\cdot 1}
x=\frac{-8\pm\sqrt{64-40}}{2}
x=\frac{-8\pm\sqrt{24}}{2}=\frac{-8\pm\sqrt{2\cdot 2\cdot 6}}{2}
x=\frac{-8\pm2\sqrt{6}}{2}=-4\pm\sqrt{6}
Hence, the two roots are -4+\sqrt{6} and -4-\sqrt{6}.
