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    $\begingroup$ Just expand left and right hand sides to the second order and Solve. $\endgroup$ Commented May 24, 2022 at 9:20
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    $\begingroup$ @umby It's preferable that you paste the equation as code, not as LaTeX. LaTex is difficult to copy into Mathematica. $\endgroup$ Commented May 24, 2022 at 9:34
  • $\begingroup$ Just start with c1=1,c2=2,c3=3. Next plot right and left side of equation. They intersect at about x=-1 and x=1/4. Use the negative value in FindRoot[Exp[-x^2]==1/(Sqrt[1-2 x]},{x,-1}] to get the negative solution. $\endgroup$ Commented May 24, 2022 at 9:49
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    $\begingroup$ Thanks for accepting my answer, but I think you were too hasty doing that. While accepting is one of the things to do after your question is answered, we recommend that users should test answers before voting and wait 24 hours after answers stop arriving before accepting the best one. That allows people in all timezones to answer your question and an opportunity for other users to point out alternatives, caveats or limitations of the available answers. $\endgroup$ Commented May 24, 2022 at 11:11
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    $\begingroup$ @DanielHuber I think the OP is expecting a closed-form expression where $x$ has been isolated of the style x == f(c1,c2,c3) and not x == f(c1,c2,c3,x). $\endgroup$ Commented May 24, 2022 at 14:15