Question 575161


{{{15x^2+26x+8=0}}} Start with the given equation.



Notice that the quadratic {{{15x^2+26x+8}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=15}}}, {{{B=26}}}, and {{{C=8}}}



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



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



{{{x = (-(26) +- sqrt( (26)^2-4(15)(8) ))/(2(15))}}} Plug in  {{{A=15}}}, {{{B=26}}}, and {{{C=8}}}



{{{x = (-26 +- sqrt( 676-4(15)(8) ))/(2(15))}}} Square {{{26}}} to get {{{676}}}. 



{{{x = (-26 +- sqrt( 676-480 ))/(2(15))}}} Multiply {{{4(15)(8)}}} to get {{{480}}}



{{{x = (-26 +- sqrt( 196 ))/(2(15))}}} Subtract {{{480}}} from {{{676}}} to get {{{196}}}



{{{x = (-26 +- sqrt( 196 ))/(30)}}} Multiply {{{2}}} and {{{15}}} to get {{{30}}}. 



{{{x = (-26 +- 14)/(30)}}} Take the square root of {{{196}}} to get {{{14}}}. 



{{{x = (-26 + 14)/(30)}}} or {{{x = (-26 - 14)/(30)}}} Break up the expression. 



{{{x = (-12)/(30)}}} or {{{x =  (-40)/(30)}}} Combine like terms. 



{{{x = -2/5}}} or {{{x = -4/3}}} Simplify. 



So the solutions are {{{x = -2/5}}} or {{{x = -4/3}}}