(Isoleren)
\(3\sqrt{q}=4\)

(Kwadrateren)
\((3\sqrt{q})^2=4^2\)
\(9q=16\)
\(q=1\frac{7}{9}\)

(Controleren)
\(q=1\frac{7}{9}\) voldoet.

(Kwadrateren)
\(t^2=-3t+54\)

(Oplossen)
\(t^2+3t-54=0\)
\((t+9)(t-6)=0\)
\(t=-9∨t=6\)

(Controleren)
\(t=-9\) voldoet niet, \(t=6\) voldoet.

(Isoleren)
\(-8x+4=4\sqrt{x}\)

(Kwadrateren)
\((-8x+4)^2=(4\sqrt{x})^2\)
\(64x^2-64x+16=16x\)

(Oplossen)
\(64x^2-80x+16=0\)
\(4x^2-5x+1=0\)
\(D=(-5)^2-4⋅4⋅1=9\)
\(x={5-\sqrt{9} \over 2⋅4}∨x={5+\sqrt{9} \over 2⋅4}\)
\(x=\frac{1}{4}∨x=1\)

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

(Isoleren)
\(t+5=\sqrt{6t+57}\)

(Kwadrateren)
\((t+5)^2=(\sqrt{6t+57})^2\)
\(t^2+10t+25=6t+57\)

(Oplossen)
\(t^2+4t-32=0\)
\((t+8)(t-4)=0\)
\(t=-8∨t=4\)

(Controleren)
\(t=4\) voldoet, \(t=-8\) voldoet niet.

(Isoleren)
\(4x-8=2\sqrt{4x-5}\)

(Kwadrateren)
\((4x-8)^2=(2\sqrt{4x-5})^2\)
\(16x^2-64x+64=4⋅(4x-5)\)
\(16x^2-64x+64=16x-20\)

(Oplossen)
\(16x^2-80x+84=0\)
\(4x^2-20x+21=0\)
\(D=(-20)^2-4⋅4⋅21=64\)
\(x={20-\sqrt{64} \over 2⋅4}∨x={20+\sqrt{64} \over 2⋅4}\)
\(x=1\frac{1}{2}∨x=3\frac{1}{2}\)

(Controleren)
\(x=1\frac{1}{2}\) voldoet niet, \(x=3\frac{1}{2}\) voldoet.