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Solve (3x - 7)^2 = (x + 4)^2.  I only found x = 11/2.

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\(\color{BrickRed} (3x - 7)^2 = (x + 4)^2\\ 9x^2-42x+49=x^2+8x+16\\ 8x^2-50x+33=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

\(x = {50 \pm \sqrt{2500-4\cdot 8\cdot 33} \over 2\cdot 8}\)

\(x=\frac{50\pm 38}{16}\)

\(x_1=\frac{11}{2}\)

\(x_2=\frac{3}{4}\)

sample

\((3x - 7)^2 = (x + 4)^2\\ (3\cdot \frac{11}{2} - 7)^2 = (\frac{11}{2} + 4)^2\\ 90.25=90.25\)   q.e.d.

\((3x - 7)^2 = (x + 4)^2\\ (3\cdot \frac{3}{4} - 7)^2 = (\frac{3}{4} + 4)^2\\ 22.5625=22.5625 \)     q.e.d.

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