The standard form of a quadratic equation is :
ax² + bx + c = 0
And the quadratic formula is:
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\).
So, first step is to compare the given equation with the above equation to get the value of a, b and c.
So, a = 9, b = 6 and c = - 17.
Next step is to plug in these values in the above formula. Therefore,
\(x=\frac{-6\pm\sqrt{6^2-4*(9)*(-17)}}{2*9}\)
\(=\frac{-6\pm\sqrt{36+612}}{18}\)
\(=\frac{-6\pm\sqrt{648}}{18}\)
\(=\frac{-6\pm\sqrt{324*2}}{18}\)
\(=\frac{-6\pm\sqrt{324}*\sqrt{2}}{18}\)
\(=\frac{-6\pm18*\sqrt{2}}{18}\)
\(=-\frac{6}{18} \pm\frac{18\sqrt{2}}{18}\)
\(=-\frac{1}{3} \pm\sqrt{2}\).
So, x = \(-\frac{1}{3} \pm\sqrt{2}\)
