```Question 196296

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 = (-(-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 the answers are {{{x = 5/3}}} or {{{x = -1}}}```