Question 154336
I'll do the first one to get you started.


# 1



{{{(5/6)x^2-7x-6/5=0}}} Start with the given equation.



{{{30((5/cross(6))x^2-7x-6/cross(5))=30(0)}}} Multiply both sides by 30 to clear the fractions.



{{{25x^2-210x-36=0}}} Distribute and multiply



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=25}}}, {{{b=-210}}}, and {{{c=-36}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-210) +- sqrt( (-210)^2-4(25)(-36) ))/(2(25))}}} Plug in  {{{a=25}}}, {{{b=-210}}}, and {{{c=-36}}}



{{{x = (210 +- sqrt( (-210)^2-4(25)(-36) ))/(2(25))}}} Negate {{{-210}}} to get {{{210}}}. 



{{{x = (210 +- sqrt( 44100-4(25)(-36) ))/(2(25))}}} Square {{{-210}}} to get {{{44100}}}. 



{{{x = (210 +- sqrt( 44100--3600 ))/(2(25))}}} Multiply {{{4(25)(-36)}}} to get {{{-3600}}}



{{{x = (210 +- sqrt( 44100+3600 ))/(2(25))}}} Rewrite {{{sqrt(44100--3600)}}} as {{{sqrt(44100+3600)}}}



{{{x = (210 +- sqrt( 47700 ))/(2(25))}}} Add {{{44100}}} to {{{3600}}} to get {{{47700}}}



{{{x = (210 +- sqrt( 47700 ))/(50)}}} Multiply {{{2}}} and {{{25}}} to get {{{50}}}. 



{{{x = (210 +- 30*sqrt(53))/(50)}}} 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 = (210+30*sqrt(53))/(50)}}} or {{{x = (210-30*sqrt(53))/(50)}}} Break up the expression.  



{{{x = (21+3*sqrt(53))/(5)}}} or {{{x = (21-3*sqrt(53))/(5)}}} Reduce


So the answers are {{{x = (21+3*sqrt(53))/(5)}}} or {{{x = (21-3*sqrt(53))/(5)}}}



which approximate to {{{x=8.568}}} or {{{x=-0.168}}}