Question 248052
{{{8x(6x+7)=-3}}} Start with the given equation.



{{{48x^2+56x=-3}}} Distribute



{{{48x^2+56x+3=0}}} Add 3 to both sides.



Notice that the quadratic {{{48x^2+56x+3}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=48}}}, {{{B=56}}}, and {{{C=3}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(56) +- sqrt( (56)^2-4(48)(3) ))/(2(48))}}} Plug in  {{{A=48}}}, {{{B=56}}}, and {{{C=3}}}



{{{x = (-56 +- sqrt( 3136-4(48)(3) ))/(2(48))}}} Square {{{56}}} to get {{{3136}}}. 



{{{x = (-56 +- sqrt( 3136-576 ))/(2(48))}}} Multiply {{{4(48)(3)}}} to get {{{576}}}



{{{x = (-56 +- sqrt( 2560 ))/(2(48))}}} Subtract {{{576}}} from {{{3136}}} to get {{{2560}}}



{{{x = (-56 +- sqrt( 2560 ))/(96)}}} Multiply {{{2}}} and {{{48}}} to get {{{96}}}. 



{{{x = (-56 +- 16*sqrt(10))/(96)}}} 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 = (-56+16*sqrt(10))/(96)}}} or {{{x = (-56-16*sqrt(10))/(96)}}} Break up the expression.  



So the solutions are {{{x = (-56+16*sqrt(10))/(96)}}} or {{{x = (-56-16*sqrt(10))/(96)}}} 



which approximate to {{{x=-0.056}}} or {{{x=-1.11}}}