Question

solve for x: 2/5 + 3/5x = x+5/10

the answers are:

x=-3

x=2

x=-3 and x=2

no solution

Answer 1

2 /5 + 3 / ( 5 x ) = ( x + 5 ) / 10
( 2 x + 3 ) / (5 x ) = ( x + 5 ) / 10
20 x + 30 = 5 x² + 25 x
5 x² + 25 x - 20 x - 30 = 0
5 x² + 5 x - 30 = 0   /:5
x² + x - 6 = 0
x² + 3 x - 2 x - 6 = 0
x ( x + 3 ) - 2 ( x + 3 ) = 0
( x + 3 ) ( x - 2 ) = 0
x 1 = - 3,  x 2 = 2
Answer:
C ) x = - 3 and x = 2