Question 617733
{{{4/x^2 = 7/(x+2)}}}


{{{4(x+2) = 7x^2}}}


{{{4x+8 = 7x^2}}}


{{{0 = 7x^2-4x-8}}}


{{{7x^2-4x-8 = 0}}}


{{{7x^2-4x-8 = 0}}}


Now use the quadratic formula to solve.


{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(-4)+-sqrt((-4)^2-4(7)(-8)))/(2(7))}}}


{{{x = (4+-sqrt(16-(-224)))/(14)}}}


{{{x = (4+-sqrt(240))/14}}}


{{{x = (4+sqrt(240))/14}}} or {{{x = (4-sqrt(240))/14}}}


{{{x = (4+4*sqrt(15))/14}}} or {{{x = (4-4*sqrt(15))/14}}}


{{{x = (2+2*sqrt(15))/7}}} or {{{x = (2-2*sqrt(15))/7}}}


So the solutions are {{{x = (2+2*sqrt(15))/7}}} or {{{x = (2-2*sqrt(15))/7}}}