Question 299442
{{{x(x-1)=2x-7}}} Start with the given equation.



{{{x^2-x=2x-7}}} Distribute



{{{x^2-x-2x+7=0}}} Get every term to the left side.



{{{x^2-3x+7=0}}} Combine like terms.



Notice that the quadratic {{{x^2-3x+7}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-3}}}, and {{{C=7}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(-3) +- sqrt( (-3)^2-4(1)(7) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-3}}}, and {{{C=7}}}



{{{x = (3 +- sqrt( (-3)^2-4(1)(7) ))/(2(1))}}} Negate {{{-3}}} to get {{{3}}}. 



{{{x = (3 +- sqrt( 9-4(1)(7) ))/(2(1))}}} Square {{{-3}}} to get {{{9}}}. 



{{{x = (3 +- sqrt( 9-28 ))/(2(1))}}} Multiply {{{4(1)(7)}}} to get {{{28}}}



{{{x = (3 +- sqrt( -19 ))/(2(1))}}} Subtract {{{28}}} from {{{9}}} to get {{{-19}}}



{{{x = (3 +- sqrt( -19 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (3 +- i*sqrt(19))/(2)}}} 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 = (3+i*sqrt(19))/(2)}}} or {{{x = (3-i*sqrt(19))/(2)}}} Break up the expression.  



So the solutions are {{{x = (3+i*sqrt(19))/(2)}}} or {{{x = (3-i*sqrt(19))/(2)}}}