Question 1049893
{{{ax^2+bx+c}}}={{{0}}}
{{{x^2+(b/a)x+c/(a)}}}={{{0}}}
{{{x^2+(b/a)x}}}={{{-c/a}}}


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

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


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

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

{{{ax^2-bx+c}}}={{{0}}}


{{{x^2-(b/a)x+c/(a)}}}={{{0}}}
{{{x^2-(b/a)x}}}={{{-c/a}}}


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

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


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


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

hence proved