Option C: ![$x=-3 \pm\sqrt{2}](/tpl/images/0512/9140/8366a.png)
Solution:
Given equation is
.
This is a quadratic equation.
Here a = 1, b = 6, c = 7
To solve the given equation by quadratic formula,
![$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}](/tpl/images/0512/9140/eb80a.png)
Substitute the given values in the quadratic formula, we get
![$x=\frac{-6 \pm \sqrt{6^{2}-4 (1) (7)}}{2 (1)}](/tpl/images/0512/9140/8b462.png)
![$x=\frac{-6 \pm \sqrt{36-28}}{2 }](/tpl/images/0512/9140/a7209.png)
![$x=\frac{-6 \pm \sqrt{8}}{2 }](/tpl/images/0512/9140/80bb4.png)
![$x=\frac{-6 \pm2 \sqrt{2}}{2 }](/tpl/images/0512/9140/3c3db.png)
![$x=\frac{2(-3 \pm\sqrt{2})}{2 }](/tpl/images/0512/9140/90c31.png)
2 in the numerator and denominator are cancelled.
![$x=-3 \pm\sqrt{2}](/tpl/images/0512/9140/8366a.png)
Option C is the correct answer.