Question

find the soution of root5x-4=2root5+6

Answer 1

√5x - 4 = 2√5 + 6
√5x - 2√5 = 10

Squaring both sides 

(√5x - 2√5)² = 10²
5x² - 20x + 20 = 100
5x² - 20x - 80 = 0
x² - 4x - 16 = 0

using sidharacharya

we get     x = 
$\frac{-(-4)+\sqrt{4^2-4*(-16)*1}}{2} \\ \\ and \\ \\ \frac{-(-4)-\sqrt{4^2-4*(-16)*1}}{2}$

so we get 
x =  ${2+2\sqrt{5}} \\ \\ and \\ \\ {2-2\sqrt{5}$

Answer 2

√5x - 4 = 2√5 + 6
√5x - 2√5 = 10

Squaring both sides 

(√5x - 2√5)² = 10²
5x² - 20x + 20 = 100                [ using (a-b)² identity]
5x² - 20x - 80 = 0
x² - 4x - 16 = 0                      [ Dividing by 5]

by quadratic formula

D=b²-4ac
=16+64
=80

X=-b-√D       or   -b+√D   
  2a                      2a

x=4-√80       0r 4 +√80   
  2                      2

x=4-4√5   or   4+4√5   
     2                  2

x=2-2√5   0r     2+2√5