We are given:
\(\displaystyle{15}={4}+{3}{w}²\)

Subtract 4 from both sides: \(\displaystyle{11}={3}{w}²\)

Divide both sides by 3: \(\displaystyle\frac{{11}}{{3}}={w}²\)

Take the square root of both sides:

\(\displaystyle\pm{\left(\sqrt{{\frac{{11}}{{3}}}}\right)}={w}\)

or

\(\displaystyle{w}=\pm\frac{\sqrt{{11}}}{\sqrt{{3}}}\)

Rationalize: \(\displaystyle{w}=\pm{\left(\frac{\sqrt{{11}}}{\sqrt{{3}}}\right)}\cdot{\left(\frac{\sqrt{{3}}}{\sqrt{{3}}}\right)}\) \(\displaystyle{w}=\pm\frac{\sqrt{{33}}}{{3}}\)

Subtract 4 from both sides: \(\displaystyle{11}={3}{w}²\)

Divide both sides by 3: \(\displaystyle\frac{{11}}{{3}}={w}²\)

Take the square root of both sides:

\(\displaystyle\pm{\left(\sqrt{{\frac{{11}}{{3}}}}\right)}={w}\)

or

\(\displaystyle{w}=\pm\frac{\sqrt{{11}}}{\sqrt{{3}}}\)

Rationalize: \(\displaystyle{w}=\pm{\left(\frac{\sqrt{{11}}}{\sqrt{{3}}}\right)}\cdot{\left(\frac{\sqrt{{3}}}{\sqrt{{3}}}\right)}\) \(\displaystyle{w}=\pm\frac{\sqrt{{33}}}{{3}}\)