Let us proceed step by step to solve the equation.

From the given equation: 6 x^{2} = 150

The next step is to factorize the given equation.

⇒ 6x^{2} - 150 = 0

On taking 6 as a common factor for the above equation we get,

⇒ 6 (x^{2} - 25) = 0

⇒ 6 (x^{2} – 5^{2}) = 0 [5^{2 }= 25]

From algebraic identities, we know that (a^{2}- b^{2}) = (a + b) (a - b)

So, the above equation becomes

⇒ 6 (x^{2} – 5^{2}) = 0

⇒ 6 (x + 5) (x - 5) = 0

⇒ x = 5, -5

### Hence, the solutions of 6x^{2 }= 150 are x = 5 and x = -5