For what values of $x$ is $\det\begin{bmatrix} x & 5\\ 7 & 10 \end{bmatrix} = 30$?

Question

If I have a matrix of the form $$ A = \begin{bmatrix} 4a & b\\ 4b & a \end{bmatrix}, $$ then $$ \left | A \right | = 4a^{2} - 4b^{2} = 4\left( a^{2} - b^{2} \right) = 4 \left( a + b \right) \left( a - b \right). $$ Now let $$ D = \begin{bmatrix} x & 5\\ 7 & 10 \end{bmatrix} $$ For what values of $x$ is $\left | D \right | = 30$?

Answer 1

Its simple $10x-35=30$ so $x=6.5$ thats all whats the problem.