<s>[INST] Determinant equation. let
A = [[x,-1],
    [3,(1-x)]]
and 
B = [[1,0,-3],
     [2,x,-6],
     [1,3,(x-5)]]
solve for x;
det(A) = det(B)
on expanding both the determinants and equating them, i obtain;
$-2x^2+3x+3 = 0$
completeing the square
$2[x^2-\frac{3x}{2}] -3 = 0$
$2[(x-\frac{3}{4})^2 - \frac{9}{16}] -3 = 0$
$2(x-\frac{3}{4})^2 - \frac{18}{16} -3 = 0$
$(x-\frac{3}{4}) = \pm \sqrt{\frac{33}{16}}$
$x = \frac{3}{4} \pm \sqrt{\frac{33}{16}}$
The answer in the back of the book is not this, could someone shed some light please.
 [/INST] You have properly solved this exercise. Actually you can simplify the result:
$$x = \frac{3 \pm \sqrt{33}}{4}$$
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