i like your way, here's another (more explanatory) approach

let revenue be R(x)

let cost be C(x)

let profit be P(x)

the revenue is the money earned from selling x units, so R(x) = 15x

the cost is...well, the cost. we pay 130000 fixed cost no matter what, plus $8 per item, so C(x) = 8x + 130000

The profit is the money we make, that is the revenue minus the cost, so

P(x) = R(x) - C(x)

=> P(x) = 15x - 8x - 130000

=> P(x) = 7x - 130000

we want a profit of 150000, that is, we want P(x) = 150000

=> P(x) = 150000 = 7x - 130000

=> 280000 = 7x

=> x = 40000

so you are correct