usepackage[table]{xcolor}
definecolor{def}{RGB}{66,103,178}
usepackage{empheq}
usepackage[most]{tcolorbox}
newtcbox{mymath}[1][]{%
    nobeforeafter, math upper, tcbox raise base,
    enhanced, colframe=blue!30!black,
    colback=def!20, boxrule=1pt,
    #1}

begin{document}

Some text…
begin{empheq}[box={mymath[colback=Bittersweet!20]}]{equation}
    (x-x_0)^2+(y-y_0)^2+(z-z_0)^2=R^2
end{empheq}

Some text…
begin{empheq}[box={mymath[colback=Bittersweet!20]}]{equation}
    x^2+y^2+z^2+Ax+By+C z=0
end{empheq}

Some text…
begin{empheq}[box={mymath[colback=Bittersweet!20]}]{equation}
    x^2+y^2+z^2=R^2
end{empheq}

end{document}