Question 101330
Starting with the general quadratic


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


the general solution using the quadratic equation is:


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




So lets solve {{{2x^2-sqrt(7)x-1=0}}} ( notice {{{a=2}}}, {{{b=-sqrt(7)}}}, and {{{c=-1}}})





{{{x = (-(-sqrt(7)) +- sqrt( (-sqrt(7))^2-4*2*-1 ))/(2*2)}}}  Plug in {{{a=2}}}, {{{b=-sqrt(7)}}}, and {{{c=-1}}}



{{{x = (sqrt(7) +- sqrt( (-sqrt(7))^2-4*2*-1 ))/(2*2)}}}  Negate {{{-sqrt(7)}}} to get {{{sqrt(7)}}}



{{{x = (sqrt(7) +- sqrt( 7-4*2*-1 ))/(2*2)}}}  Square {{{-sqrt(7)}}} to get 7



{{{x = (sqrt(7) +- sqrt( 7+8 ))/(2*2)}}}  Multiply {{{-4*2*-1}}} to get {{{8}}}




{{{x = (sqrt(7) +- sqrt( 15 ))/(2*2)}}}  Add



{{{x = (sqrt(7) +- sqrt( 15 ))/(4)}}}  Multiply



{{{x = (sqrt(7) + sqrt( 15 ))/(4)}}} or {{{x = (sqrt(7) - sqrt( 15 ))/(4)}}}  Break up the expression



So the answer is:


{{{x = (sqrt(7) + sqrt( 15 ))/(4)}}} or {{{x = (sqrt(7) - sqrt( 15 ))/(4)}}}