Question 259236
the solutions of a general quadratic equation {{{ax^2+bx+c}}} are given by the quadratic formula

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

in your question x^2+6x=-3  that is x^2+6x+3=0

we have a=1, b=6, c=3

so the solutions are {{{x=(-6 +- sqrt(36-4*1*3))/2 }}}
                      
                    =>{{{ x=(-6 +- sqrt(24))/2 }}}
                    =>{{{ x=(-6 +- 2sqrt(6))/2 }}}
                    =>{{{ x=(-3 +- sqrt(6)) }}}