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If I have a quadratic $Ax^2 + Bx + C$ where the coefficients contain an additional unknown $u$ for

$Ax^2+(bu+c)x+(du^2+eu+g)$

where $A$, $b$, $c$, $d$, $e$, $g$ are known

Is there a way to find solutions for $x$ and $u$ that satisfies

$0 = Ax^2+(bu+c)x+(du^2+eu+g)$

Blindman67
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    In general, the latter is equation of a conic section. Can you provide the known constants? – user376343 Jul 27 '20 at 13:52
  • @user376343 The constants are derived. eg $A = -2lxvx - 2lyvy + vx^2 + lx^2 + vy^2 + ly^2$ where $vx,vy$ and $lx,ly$ are two vectors and the others will not fit in the comment but are derived from an additional vector, 3 coordinate pairs and a scalar. I am trying to solve a moving ball intercepting a moving line (both movements are linear) $x$ is tine of intercept, and $u$ is unit position on line of intercept. – Blindman67 Jul 27 '20 at 14:13

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