<PRE><B>Question 154390</B>
6x + 7 = 20/x
;
Multiply both sides by x to get rid of the denominator
x(6x + 7) = 20
:
Mult terms inside the brackets:
6x^2 + 7x = 20
;
Subtract 20 from both sides to reveal our old friend, the quadratic equation
6x^2 + 7x - 20 = 0
:
With diligent effort we can factor this to:
(2x + 5)(3x - 4) = 0
Two solutions
2x = -5
x = {{{-5/2}}}
x = -2.5
and
3x = 4
x = {{{4/3}}}
;
:
Check the 1st solution in the original equation
6(-2.5) + 7 = {{{20/-2.5}}}
-15 + 7 = -8
;
Check the 2nd solution
6*{{{4/3}}} + 7 = {{{20(3/4)}}}
8 + 7 = 15</PRE>