Question

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)

Answer 1

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 !