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

(Kwadrateren)
\((6 \sqrt{x})^{2} = 2^{2}\)
\(36 x = 4\)
\(x = \frac{1}{9}\)

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

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

(Oplossen)
\(1 x^{2} + -4 x + -12 = 0\)
\((x + 2) (x + -6) = 0\)
\(x = -2 ∨ x = 6\)

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

(Isoleren)
\(5 x - 2 = 3 \sqrt{x}\)

(Kwadrateren)
\((5 x - 2)^{2} = (3 \sqrt{x})^{2}\)
\(25 x^{2} - 20 x + 4 = 9 x\)

(Oplossen)
\(25 x^{2} + -29 x + 4 = 0\)
\(D = -29^{2} - 4 ⋅ 25 ⋅ 4 = 441\)
\(x = {29 - \sqrt{441} \over 2 ⋅ 25} ∨ x = {29 + \sqrt{441} \over 2 ⋅ 25}\)
\(x = {4 \over 25} ∨ x = 1\)

(Controleren)
\(x = \frac{4}{25}\) voldoet niet, \(x = 1\) voldoet.

(Isoleren)
\(x + 5 = \sqrt{8 x + 60}\)

(Kwadrateren)
\((x + 5)^{2} = (\sqrt{8 x + 60})^{2}\)
\(x^{2} + 10 x + 25 = 8 x + 60\)

(Oplossen)
\(1 x^{2} + 2 x + -35 = 0\)
\((x + 7) (x + -5) = 0\)
\(x = -7 ∨ x = 5\)

(Controleren)
\(x = -7\) voldoet niet, \(x = 5\) voldoet.

(Isoleren)
\(3 x - 7 = 2 \sqrt{2 x - 5}\)

(Kwadrateren)
\((3 x - 7)^{2} = (2 \sqrt{2 x - 5})^{2}\)
\(9 x^{2} - 42 x + 49 = 4 ⋅ (2 x - 5)\)
\(9 x^{2} - 42 x + 49 = 8 x - 20\)

(Oplossen)
\(9 x^{2} + -50 x + 69 = 0\)
\(D = -50^{2} - 4 ⋅ 9 ⋅ 69 = 16\)
\(x = {50 - \sqrt{16} \over 2 ⋅ 9} ∨ x = {50 + \sqrt{16} \over 2 ⋅ 9}\)
\(x = {23 \over 9} ∨ x = 3\)

(Controleren)
Beide oplossingen voldoen.