still need working of this equation to the root,it is urgent, this is simultaneous equation 3x+2y=14....(1) and 2xy+5=21?

From (1) we can express 3x in terms of 2y. 14-3x = 2y..(2). Your second
equation is 2xy+5 = 21, ie., x(2y) = 16. Substitute 14-3x for 2y in this equation getting x(14-3x) = 16, ie., 3x^2 -14x +16 = 0, ie., (x-2)(3x-8) = 0,
ie., x = (8/3) or 2. By (2), y= (1/2)(14-3x). Then y = (1/2)[(14-8) or (14-6)]
= (1/2)[6 or 8] = 3 or 4. .Solutions are (x,y) = (8/3 , 3) & (2 , 4).

Rearrange the second equation 2xy = 16 then xy = 8 then x = 8/y

now substitute into 1)

3(8/y) + 2y = 14 and we have a nice quadratic equation.

24/y + 2y = 14
24 + 2y^2 = 14y (just multiply by y)

halving both sides
12 + y^2 = 7y rearranging
y^2 -7y + 12 = 0
(y-4) (y-3) = 0
either y = 4 or y = 3

substituting y = 4 into (1)

3x + 2*4 = 14
3x + 8 = 14
3x = 6
x = 2

So x =2, y = 4 is a solution.

Substituting y = 3 into 3x + 2y = 14
3x + 6 = 14
3x = 8
x = 8/3

So either x = 8/3 and y = 3 or x =2, y = 4 <<< ANSWER!

let's see if these solutions are correct.

Checking x = 8/3 and y = 3
2xy + 5 = 21
2(8/3)(3) + 5 = 21
2*8 + 5 = 21
16+5 = 21 this is correct.

Checking x =2, y = 4

2xy + 5 = 21
2*2*4 + 5 = 21
4*4 + 5 = 21
16 + 5 = 21
this is also correct.

2*y = 14 - 3*x from (1)
Substitute for 2*y into (2)
x*(14 - x) + 5 = 21
-x^2 + 14*x - 16 = 0
x^2 - 14*x + 16 = 0
Solve quadratic by formula method
x = (1/2)*(14 +- sqrt(14^2 - 4*16))
= (1/2)*(14 +- sqrt(130))

x1 = (1/2)*(14 + sqrt(130))
x2 = (1/2)*(14 - sqrt(130))

y = (1/2)*(14 - 3*x)

y1 = (1/2)*(14 - 3*x1)
y2 = (1/2)*(14 - 3*x2)


(x,y) = (x1,y1) or (x2,y2)