Question 25681
{{{-p/2}}}±{{{ sqrt( p^2/4-q ) }}}


let p={{{b/a}}} and q={{{c/a}}}

It says that it can be derived by "completing" the square of a quadratic equation.  A response to this problem would really make my day!  

-------------------------------------------------------------------------------
SUBSTITUTE IN THE ANSWER GIVEN BELOW YOUR NOMENCLATURE THAT 
 p={{{b/a}}} and q={{{c/a}}}..AND YOU WILL GET YOUR ANSWER
LET THE QUADRATIC BE
 AX^2+BX+C=0...SINCE THIS IS A QUADRATIC ,A IS NOT EQUAL TO ZERO..SO DIVIDING WITH A WE GET 
X^2+BX/A+C/A=0
WRITE IT AS A PERFECT SQUARE USING X^2 AND X TERMS
{X^2+2*X*(B/2A)+(B/2A)^2}-(B/2A)^2+C/A=0 
{X+(B/2A)}^2=(B/2A)^2-C/A=B^2/4A^2-C/A=(B^2-4AC)/4A^2
TAKING SQUARE ROOT 
X+B/2A={{{(PLUS OR MINUS sqrt( B^2-4*A*C ))/(2*A) }}} 
OR
{{{x = (-B +- sqrt( B^2-4*A*C ))/(2*A) }}} 
THIS IS THE GENERAL METHOD OF DERIVATION OF ROOTS OF A QUADRATIC EQUATION.