The solve function with floating-point numbers works by converting the floating-point numbers to approximate rationals, calling solve with these converted arguments, and converting the results back to floating-point numbers using evalf.

This can be convenient for solving equations with a combination of floating-point numbers and parameters (since fsolve will not solve equations with unassigned parameters).  In most cases, it is a better idea to convert the input into exact values manually since this will generally give more meaningful answers.

$\mathrm{eq}≔x^2-3x+0.01\:$

$\mathrm{solve}\left(\mathrm{eq}\,x\right)$

$2.996662955,0.00333704529$

$\mathrm{eqe}≔\mathrm{convert}\left(\mathrm{eq}\,'\mathrm{rational}'\,'\mathrm{exact}'\right)$

$\mathrm{eqe}≔x^2-3x+\frac{1}{100}$

$\mathrm{sol}≔\mathrm{solve}\left(\mathrm{eqe}\,x\right)$

$\mathrm{sol}≔\frac{3}{2}+\frac{2\sqrt{14}}{5},\frac{3}{2}-\frac{2\sqrt{14}}{5}$

$\mathrm{evalf}\left(\mathrm{sol}\right)$

$2.996662955,0.003337045$

$\mathrm{solve}\left(\left\{3.7y+z=\sin \left(x\right)\,x^2-y=z\right\}\,\left\{y\,z\right\}\right)$

$\left\{y=-0.3703703704x^2+0.3703703704\sin \left(x\right)\,z=1.370370370x^2-0.3703703704\sin \left(x\right)\right\}$

$\mathrm{fsolve}\left(\left\{3.7y+z=\sin \left(x\right)\,x^2-y=z\right\}\,\left\{y\,z\right\}\right)$

Error, (in fsolve) x is in the equation, and is not solved for