question_answer

Solve for x:  \[2{{x}^{2}}+6\sqrt{3}x-60=0\]

Answer:

Consider the given equation

\[2{{x}^{2}}+6\sqrt{3}x-60=0\]

\[\Rightarrow {{x}^{2}}+3\sqrt{3}x-30=0\]                          ?(i)

Comparing equation (i) by

\[a{{x}^{2}}+bx+c=0\]

We get               \[a=1,b=3\sqrt{3},c=-30\].

By quadratic formula

\[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\]

\[x=\frac{-3\sqrt{3}\pm \sqrt{27+120}}{2}\]

\[x=\frac{-3\sqrt{3}\pm \sqrt{147}}{2}\]

Hence value for \[x=\frac{-3\sqrt{3}\pm \sqrt{147}}{2}\]