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 !