Question 172418


{{{3x^2+2x=-5-4x}}} Start with the given equation.



{{{3x^2+2x+5+4x=0}}} Get all terms to the left side.



{{{3x^2+6x+5=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=3}}}, {{{b=6}}}, and {{{c=5}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(6) +- sqrt( (6)^2-4(3)(5) ))/(2(3))}}} Plug in  {{{a=3}}}, {{{b=6}}}, and {{{c=5}}}



{{{x = (-6 +- sqrt( 36-4(3)(5) ))/(2(3))}}} Square {{{6}}} to get {{{36}}}. 



{{{x = (-6 +- sqrt( 36-60 ))/(2(3))}}} Multiply {{{4(3)(5)}}} to get {{{60}}}



{{{x = (-6 +- sqrt( -24 ))/(2(3))}}} Subtract {{{60}}} from {{{36}}} to get {{{-24}}}



{{{x = (-6 +- sqrt( -24 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (-6 +- 2i*sqrt(6))/(6)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-6+2i*sqrt(6))/(6)}}} or {{{x = (-6-2i*sqrt(6))/(6)}}} Break up the expression.  



So the answers are {{{x = (-6+2i*sqrt(6))/(6)}}} or {{{x = (-6-2i*sqrt(6))/(6)}}}