Question 878849
<pre>
{{{(sqrt(6))x^2+2x-sqrt(3/2)}}}{{{""=""}}}{{{"0"}}}

Simplify {{{sqrt(3/2))}}}{{{""=""}}}{{{sqrt((3*2)/(2*2))}}}{{{""=""}}}{{{sqrt(6)/sqrt(4)}}}{{{""=""}}}{{{sqrt(6)/2}}}

{{{(sqrt(6))x^2+2x-sqrt(6)/2}}}{{{""=""}}}{{{"0"}}}

Clear the fraction by multiplying through by 2

{{{(2sqrt(6))x^2+4x-sqrt(6)}}}{{{""=""}}}{{{"0"}}}

Use the quadratic formula:

{{{x}}}{{{""=""}}}{{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

with

{{{a=2sqrt(6)}}}, {{{b=4}}}, {{{c=-sqrt(6)}}}

{{{x}}}{{{""=""}}}{{{(-(4) +- sqrt( (4)^2-4*(2sqrt(6))*(-sqrt(6)) ))/(2*(2sqrt(6))) }}}

{{{x}}}{{{""=""}}}{{{(-4 +- sqrt(16+48))/(4*sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{(-4 +- sqrt(64))/(4*sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{(-4 +- 8)/(4*sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{(-4 +- 8)/(4*sqrt(6)) }}}

Using the +

{{{x}}}{{{""=""}}}{{{(-4 + 8)/(4sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{4/(4*sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{1/(sqrt(6))) }}}

{{{x}}}{{{""=""}}}{{{(1/(sqrt(6)))(sqrt(6)/sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{sqrt(6)/6}}}

Using the -

{{{x}}}{{{""=""}}}{{{(-4 - 8)/(4sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{-12/(4*sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{-3/(sqrt(6))) }}}

{{{x}}}{{{""=""}}}{{{(-3/(sqrt(6)))(sqrt(6)/sqrt(6)) }}}

{{{x}}}{{{""=""}}}{{{-3sqrt(6)/6}}}

{{{x}}}{{{""=""}}}{{{-sqrt(6)/2}}}

Two solutions:  {{{sqrt(6)/6}}}, {{{-sqrt(6)/2}}}

Edwin</pre>