Solve the following quadratic equations :
(i)` 9x^(2) - 8x+2=0`
(ii) ` sqrt7 x^(2) +x+ sqrt7=0`
(iii)` 2sqrt3x^(2) -sqrt2 x + 3sqrt3 =0`

Explanation

(i) ` 9x^(2) -8x +2=0`
Here, `b^(2) -4ac = (-8)^(2) - 4(9)(2)`
= 64 -72 = -8
The solutions of the equation are given by
`= ((-8)+-sqrt(-8))/18 = (8+-2sqrt2i)/18 = (4+-sqrt2i)/9`
(ii) ` sqrt7x^(2)+x+sqrt7=0`
Here ` , b^(2) -4ac = (1)^(2) -4(sqrt7)(sqrt7)`
= 1-28 = -27
The solutions of the euquation are given by
`((-1)+-sqrt(-27))/(2sqrt7) = (-1 +-3sqrt3i)/(2sqrt7)`
(iii)` 2sqrt3x^(2) -sqrt3x +3sqrt3=0`
Here, ` b^(2) -4ac = (-sqrt2)^(2)-4(2sqrt3)(3sqrt3)`
= 2- 72 =-70
The solutions of the equation are given by ` ( -(-sqrt2)+- sqrt(-70))/(4sqrt3)`
`= (sqrt2 +- sqrt70i)/(4sqrt3)`