Question 147538


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



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



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=3}}}, {{{b=-2}}}, 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 = (-(-2) +- sqrt( (-2)^2-4(3)(-5) ))/(2(3))}}} Plug in  {{{a=3}}}, {{{b=-2}}}, and {{{c=-5}}}



{{{x = (2 +- sqrt( (-2)^2-4(3)(-5) ))/(2(3))}}} Negate {{{-2}}} to get {{{2}}}. 



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



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



{{{x = (2 +- sqrt( 4+60 ))/(2(3))}}} Rewrite {{{sqrt(4--60)}}} as {{{sqrt(4+60)}}}



{{{x = (2 +- sqrt( 64 ))/(2(3))}}} Add {{{4}}} to {{{60}}} to get {{{64}}}



{{{x = (2 +- sqrt( 64 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (2 +- 8)/(6)}}} Take the square root of {{{64}}} to get {{{8}}}. 



{{{x = (2 + 8)/(6)}}} or {{{x = (2 - 8)/(6)}}} Break up the expression. 



{{{x = (10)/(6)}}} or {{{x =  (-6)/(6)}}} Combine like terms. 



{{{x = 5/3}}} or {{{x = -1}}} Simplify. 



So our answers are {{{x = 5/3}}} or {{{x = -1}}}