Question 195871
{{{2y^2-6y-8=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ay^2+by+c}}} where {{{a=2}}}, {{{b=-6}}}, and {{{c=-8}}}



Let's use the quadratic formula to solve for y



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



{{{y = (-(-6) +- sqrt( (-6)^2-4(2)(-8) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=-6}}}, and {{{c=-8}}}



{{{y = (6 +- sqrt( (-6)^2-4(2)(-8) ))/(2(2))}}} Negate {{{-6}}} to get {{{6}}}. 



{{{y = (6 +- sqrt( 36-4(2)(-8) ))/(2(2))}}} Square {{{-6}}} to get {{{36}}}. 



{{{y = (6 +- sqrt( 36--64 ))/(2(2))}}} Multiply {{{4(2)(-8)}}} to get {{{-64}}}



{{{y = (6 +- sqrt( 36+64 ))/(2(2))}}} Rewrite {{{sqrt(36--64)}}} as {{{sqrt(36+64)}}}



{{{y = (6 +- sqrt( 100 ))/(2(2))}}} Add {{{36}}} to {{{64}}} to get {{{100}}}



{{{y = (6 +- sqrt( 100 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{y = (6 +- 10)/(4)}}} Take the square root of {{{100}}} to get {{{10}}}. 



{{{y = (6 + 10)/(4)}}} or {{{y = (6 - 10)/(4)}}} Break up the expression. 



{{{y = (16)/(4)}}} or {{{y =  (-4)/(4)}}} Combine like terms. 



{{{y = 4}}} or {{{y = -1}}} Simplify. 



So the answers are {{{y = 4}}} or {{{y = -1}}}