By the midpoint formula,

Substitute the values in given equation:
$\text{LHS} = 6 \Big( \frac{3}{2}\Big) + (-1)-8$
$\implies \text{LHS}= 9-1 -8 =0 =\text{RHS}$
Since both sides are equal, this proves the equation $\sf{6 \alpha \: + \: \beta \: - 8 \: = 0}$