Find the value of `lambda " if " 2x^(2) +6xy +3y^(2) +8x +14y +lambda =0` represent a pair of straight lines.

Explanation

`ax^(2) +2hxy+ by^(2) 2gx + 2fy+ c=0` represents a pair of lines if
`|{:(a,,h,,g),(h,,b,,f),(g,,f,,c):}|=0`
`rArr|{:(2,,7//2,,4),(7//2,,3,,7),(4,,7,,lambda):}|=0`
`" or " 6lambda +2(7) (4) ((7)/(2)) -2(7)^(2) -3 (4)^(2) -lambda ((7)/(2))^(2) =0`
`" or " 6 lambda +196 -98 -48 -(49lambda)/(4)=0`
`" or " (49lambda)/(4)-6lambda =196 -146 =50`
`" or " (25lambda)/(4)=50 " or " lambda =(200)/(25)=8`