(Isoleren)
\(2 \sqrt{x} = 4\)

(Kwadrateren)
\((2 \sqrt{x})^{2} = 4^{2}\)
\(4 x = 16\)
\(x = 4\)

(Controleren)
\(x = 4\) voldoet.

(Kwadrateren)
\(x^{2} = -4 x + 12\)

(Oplossen)
\(x^{2} + 4 x - 12 = 0\)
\((x + 6) (x - 2) = 0\)
\(x = -6 ∨ x = 2\)

(Controleren)
\(x = -6\) voldoet niet, \(x = 2\) voldoet.

(Isoleren)
\(6 x - 8 = -2 \sqrt{x}\)

(Kwadrateren)
\((6 x - 8)^{2} = (-2 \sqrt{x})^{2}\)
\(36 x^{2} - 96 x + 64 = 4 x\)

(Oplossen)
\(36 x^{2} - 100 x + 64 = 0\)
\(9 x^{2} - 25 x + 16 = 0\)
\(D = (-25)^{2} - 4 ⋅ 9 ⋅ 16 = 49\)
\(x = {25 - \sqrt{49} \over 2 ⋅ 9} ∨ x = {25 + \sqrt{49} \over 2 ⋅ 9}\)
\(x = 1 ∨ x = 1\frac{7}{9}\)

(Controleren)
\(x = 1\) voldoet, \(x = 1\frac{7}{9}\) voldoet niet.

(Isoleren)
\(x + 2 = \sqrt{3 x + 60}\)

(Kwadrateren)
\((x + 2)^{2} = (\sqrt{3 x + 60})^{2}\)
\(x^{2} + 4 x + 4 = 3 x + 60\)

(Oplossen)
\(x^{2} + x - 56 = 0\)
\((x + 8) (x - 7) = 0\)
\(x = -8 ∨ x = 7\)

(Controleren)
\(x = 7\) voldoet, \(x = -8\) voldoet niet.

(Isoleren)
\(4 x - 9 = 3 \sqrt{2 x - 2}\)

(Kwadrateren)
\((4 x - 9)^{2} = (3 \sqrt{2 x - 2})^{2}\)
\(16 x^{2} - 72 x + 81 = 9 ⋅ (2 x - 2)\)
\(16 x^{2} - 72 x + 81 = 18 x - 18\)

(Oplossen)
\(16 x^{2} - 90 x + 99 = 0\)
\(D = (-90)^{2} - 4 ⋅ 16 ⋅ 99 = 1\,764\)
\(x = {90 - \sqrt{1\,764} \over 2 ⋅ 16} ∨ x = {90 + \sqrt{1\,764} \over 2 ⋅ 16}\)
\(x = 1\frac{1}{2} ∨ x = 4\frac{1}{8}\)

(Controleren)
\(x = 1\frac{1}{2}\) voldoet niet, \(x = 4\frac{1}{8}\) voldoet.