Question

Solve for x:

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

Answer 1

Consider the given equation $2x^2+6\sqrt{3}x-60=0$

$\Rightarrow x^2+3\sqrt{3}x-30=0$

Comparing equation (i) by $a{x}^2+bx+c=0$

We get $a=1,b=3\sqrt{3},c=-30$

By quadratic formula

$x=\frac{-b\pm \sqrt{b^2-4ax}}{2a}$

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

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

$x=\frac{-3\sqrt{3}\pm 7\sqrt{3}}{2}$

$x=\frac{-3\sqrt{3}+7\sqrt{3}}{2}or\frac{-3\sqrt{3}-7\sqrt{3}}{2}$

$x=\frac{4\sqrt{3}}{2}or\frac{-10\sqrt{3}}{2}$

$x=2\sqrt{3}or-5\sqrt{3}$

Hence value for $x=2\sqrt{3}or-5\sqrt{3}$