You can put this solution on YOUR website! Okay, from
14y^2 + 1 = 6y^2 + 7y
let's gather everything on the left, and get
8y^2 - 7y + 1 = 0
This does not factor over the rational numbers so we use the quadratic formula to get
y = (7 +/- sqrt(17)) / 16
but I suspect there is a mistake somewhere in the problem...
You can put this solution on YOUR website! 14y^2+1=6y^2+7y
8y^2-7y+1=0
y=(1/16)(7+/- (49-32)
y=(1/16)(7+/- sqrt (17)
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numerically, this is about 0.69 and 0.18