Question 154171
You can solve by 1) factoring, 2) quadratic formula, and 3) completing the square. I'll do the second technique to get you started





{{{12x^2-10x-42=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=12}}}, {{{b=-10}}}, and {{{c=-42}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-10) +- sqrt( (-10)^2-4(12)(-42) ))/(2(12))}}} Plug in  {{{a=12}}}, {{{b=-10}}}, and {{{c=-42}}}



{{{x = (10 +- sqrt( (-10)^2-4(12)(-42) ))/(2(12))}}} Negate {{{-10}}} to get {{{10}}}. 



{{{x = (10 +- sqrt( 100-4(12)(-42) ))/(2(12))}}} Square {{{-10}}} to get {{{100}}}. 



{{{x = (10 +- sqrt( 100--2016 ))/(2(12))}}} Multiply {{{4(12)(-42)}}} to get {{{-2016}}}



{{{x = (10 +- sqrt( 100+2016 ))/(2(12))}}} Rewrite {{{sqrt(100--2016)}}} as {{{sqrt(100+2016)}}}



{{{x = (10 +- sqrt( 2116 ))/(2(12))}}} Add {{{100}}} to {{{2016}}} to get {{{2116}}}



{{{x = (10 +- sqrt( 2116 ))/(24)}}} Multiply {{{2}}} and {{{12}}} to get {{{24}}}. 



{{{x = (10 +- 46)/(24)}}} Take the square root of {{{2116}}} to get {{{46}}}. 



{{{x = (10 + 46)/(24)}}} or {{{x = (10 - 46)/(24)}}} Break up the expression. 



{{{x = (56)/(24)}}} or {{{x =  (-36)/(24)}}} Combine like terms. 



{{{x = 7/3}}} or {{{x = -3/2}}} Simplify. 



So the answers are {{{x = 7/3}}} or {{{x = -3/2}}}