Question 102544
{{{5x^2+5x=3}}} Start with the given equation



{{{5x^2+5x-3=0}}} Subtract 3 from both sides





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 {{{5*x^2+5*x-3=0}}} ( notice {{{a=5}}}, {{{b=5}}}, and {{{c=-3}}})





{{{x = (-5 +- sqrt( (5)^2-4*5*-3 ))/(2*5)}}} Plug in a=5, b=5, and c=-3




{{{x = (-5 +- sqrt( 25-4*5*-3 ))/(2*5)}}} Square 5 to get 25  




{{{x = (-5 +- sqrt( 25+60 ))/(2*5)}}} Multiply {{{-4*-3*5}}} to get {{{60}}}




{{{x = (-5 +- sqrt( 85 ))/(2*5)}}} Combine like terms in the radicand (everything under the square root)





{{{x = (-5 +- sqrt(85))/10}}} Multiply 2 and 5 to get 10



So our answer is:



{{{x = (-5 +- sqrt(85))/10}}}