What are the solutions of the equation x^2-30=x in x=-6,x=-5 x=-6,x=5 x=-5,x=6 x=5,x=6

To solve the equation $$x^2 - 30 = x$$ , we can rearrange the equation to $$x^2 - x - 30 = 0$$ . This is a quadratic equation in the form of $$ax^2 + bx + c = 0$$ , where $$a = 1$$ , $$b = -1$$ , and $$c = -30$$ .

We can solve this quadratic equation by factoring. We need to find two numbers whose product is $$ac = -30$$ and whose sum is $$b = -1$$ . The two numbers that satisfy these conditions are $$-6$$ and $$5$$ .

So, we can factor the quadratic equation as $$(x - 6)(x + 5) = 0$$ .

Setting each factor equal to zero gives us the solutions:
$$x - 6 = 0$$ or $$x + 5 = 0$$

Solving for $$x$$ , we get:
$$x = 6$$ or $$x = -5$$

Therefore, the solutions to the equation $$x^2 - 30 = x$$ are $$x = 6$$ and $$x = -5$$ .

So, the correct answer is $$x = -5, x = 6$$ .