Question 417641
{{{(x-1)/4=5/(x+7)}}} Start with the given equation.



{{{(x-1)(x+7)=5*4}}} Cross multiply



{{{(x-1)(x+7)=20}}} Multiply



{{{x^2+6x-7=20}}} FOIL



{{{x^2+6x-7-20=0}}} Subtract 20 from both sides.



{{{x^2+6x-27=0}}} Combine like terms.



Notice that the quadratic {{{x^2+6x-27}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=6}}}, and {{{C=-27}}}



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



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



{{{x = (-(6) +- sqrt( (6)^2-4(1)(-27) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=6}}}, and {{{C=-27}}}



{{{x = (-6 +- sqrt( 36-4(1)(-27) ))/(2(1))}}} Square {{{6}}} to get {{{36}}}. 



{{{x = (-6 +- sqrt( 36--108 ))/(2(1))}}} Multiply {{{4(1)(-27)}}} to get {{{-108}}}



{{{x = (-6 +- sqrt( 36+108 ))/(2(1))}}} Rewrite {{{sqrt(36--108)}}} as {{{sqrt(36+108)}}}



{{{x = (-6 +- sqrt( 144 ))/(2(1))}}} Add {{{36}}} to {{{108}}} to get {{{144}}}



{{{x = (-6 +- sqrt( 144 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-6 +- 12)/(2)}}} Take the square root of {{{144}}} to get {{{12}}}. 



{{{x = (-6 + 12)/(2)}}} or {{{x = (-6 - 12)/(2)}}} Break up the expression. 



{{{x = (6)/(2)}}} or {{{x =  (-18)/(2)}}} Combine like terms. 



{{{x = 3}}} or {{{x = -9}}} Simplify. 



So the solutions are {{{x = 3}}} or {{{x = -9}}} 



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