How many solutions can be found for the linear equation?

How many solutions can be found for the linear equation?

4(x + 5) - 5 = 2/(8x + 18)

1 Answer
Jul 25, 2018

There is 2 solutions :

#x_1=-(3+sqrt(5/2)/2)#

#x_2=-3+sqrt(5/2)/2#

See explanations below

Explanation:

#4(x+5)-5=2/(8x+18)#
#4x+20-5=2/(8x+18)#

#D_f: x in RR# \ #{-9/4}#

#(4x+15)(8x+18)=2#

#32x^2+120x+72x+270=2#

#32x^2+192x+268=0#

#8x^2+48x+67=0#

#x^2+6x+67/8=0#

it's a second degree equation like : #ax^2+bx+c=0#

with #a=1#, #b=6#, #c=67/8#

So : #Delta=b^2-4ac#

And : #x=(-b+-sqrt(Delta))/(2a)#

#Delta=6^2-4*1*67/8#

#Delta=36-67/2#
#Delta=5/2#

#x_1=-(6+sqrt(5/2))/2#

#x_2=(-6+sqrt(5/2))/2#

#x_1=-(3+sqrt(5/2)/2)#

#x_2=-3+sqrt(5/2)/2#

\0/ here's our answer !