Question 196541
{{{3x^2-2x=15x-10}}} Start with the given equation.



{{{3x^2-2x-15x+10=0}}} Get all terms to the left side.



{{{3x^2-17x+10=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=3}}}, {{{b=-17}}}, and {{{c=10}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-17) +- sqrt( (-17)^2-4(3)(10) ))/(2(3))}}} Plug in  {{{a=3}}}, {{{b=-17}}}, and {{{c=10}}}



{{{x = (17 +- sqrt( (-17)^2-4(3)(10) ))/(2(3))}}} Negate {{{-17}}} to get {{{17}}}. 



{{{x = (17 +- sqrt( 289-4(3)(10) ))/(2(3))}}} Square {{{-17}}} to get {{{289}}}. 



{{{x = (17 +- sqrt( 289-120 ))/(2(3))}}} Multiply {{{4(3)(10)}}} to get {{{120}}}



{{{x = (17 +- sqrt( 169 ))/(2(3))}}} Subtract {{{120}}} from {{{289}}} to get {{{169}}}



{{{x = (17 +- sqrt( 169 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (17 +- 13)/(6)}}} Take the square root of {{{169}}} to get {{{13}}}. 



{{{x = (17 + 13)/(6)}}} or {{{x = (17 - 13)/(6)}}} Break up the expression. 



{{{x = (30)/(6)}}} or {{{x =  (4)/(6)}}} Combine like terms. 



{{{x = 5}}} or {{{x = 2/3}}} Simplify. 



So the answers are {{{x = 5}}} or {{{x = 2/3}}}