I used Mathway to find x in the equation
$-1.9497137966666855 * x^2 + 0.0 * x - 1 = -0.6556211074636167 * x^2 + 0.0*x - 5$
it gave the answer $1.75811509$ and $-1.75811509$
but when I replace one of these values with $x$, for example if I plug $x = 1.75811509$ into $-1.9497137966666855 * x^2 + 0.0 * x - 1$ which is
$$-1.9497137966666855 * 1.75811509^2 + 0.0*1.75811509 - 1$$
it gives the value of $-7.02650426$ instead of $0$ (zero)
You have, $$\rm{LHS}=-1.9497137966666855(1.75811509)^2-1=\color{blue}{-7.026504}2603506961$$ and $$\rm{RHS}=-0.6556211074636167(1.75811509)^2-5=\color{blue}{-7.026504}302354686$$ which indeed verifies $\rm{LHS}=\rm{RHS}$ upto certain precision. The $\rm{LHS}$ or the $\rm{RHS}$ doesn't have to be zero necessarily.
Hope this helps. :)