Question 1209315
f(x) = (4x - 1)/(5x + 2) + x/(x + 5).
For what value of a is f(a) = 3?

{{{f(x) = ((4x - 1)/(5x + 2)) + (x/(x + 5))}}}


{{{f(a) = ((4a- 1)/(5a + 2)) + (a/(a + 5))}}}



{{{((4a- 1)/(5a + 2)) + (a/(a + 5))= 3}}}

multiply equation by (5a+2)(a+5)

(4a-1)(a+5)+a*(5a+2) =3(5a+2)(a+5)

= 
4a^2+19a-5+5a^2+2a  = 15a^2+81a+30

9a^2+21a-5 = 15a^2+81a+30

6a^2+60a+35 =0

SUse formula method

a= 6 , b= 60 ,c = 35

b^2-4ac = 60^2- 4*6*35 = 3600-840 =2760

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



{{{a = (-60 +- sqrt(2760))/12 }}}


{{{a = (-60+-2*sqrt(690))/12 }}}


{{{a= (-30 +-sqrt(690))/6}}}