We are given that,

We need to find the value of x.

Determinant of 2 × 2 matrix is found as,

Let us take left hand side (LHS) of the given matrix equation.

⇒ LHS = 2x × x – 5 × 8

⇒ LHS = 2x² – 40

Let us take right hand side (RHS) of the given matrix equation.

⇒ RHS = 6 × 3 – (-2) × 7

⇒ RHS = 18 – (-14)

⇒ RHS = 18 + 14

⇒ RHS = 32

Now,

LHS = RHS

⇒ 2x² – 40 = 32

⇒ 2x² = 32 + 40

⇒ 2x² = 72

⇒ x² = 36

⇒ x = ±√36

⇒ x = ±6

Thus, the value of x is ±6.