How can I solve these following equations:

x2 - x - 6 = 0

4x2 - 5x = 0

x2 = 3x2 + 13999

3x2 = x2 + 13999

2. These are quadratic equations. You solve them by factorising. The coefficient of x^2 is called a, the coefficient of x is called b, and the constant is called c.

1. Find ac.
2. Find the factors of ac which add and make b.
3. Rewrite the bx term using these factors.
4. Factorise the first and last terms.
5. Find the common factor, put that in the first bracket.
6. Put what is left in the second bracket.

I'll do the first one for you.

$x^2 -x -6 = 0$

a = 1
b = -1
c = -6

1. $ac = -6$

2. $2 * -3 = -6$

$2 + -3 = -1$

3. $x^2 + 2x -3x -6 = 0$

4. $x(x + 2) -3 (x + 2) = 0$

5. $(x + 2)$

6. $(x + 2)(x - 3) = 0$

Now you have factorised it. Now one of the brackets must equal 0, as anything multiplied by 0 = 0.

So for the first bracket to equal 0, x would have to be -2, as -2 + 2 = 0
For the second would it would have to be 3, as 3 - 3 = 0.

So your solutions are x = -2, and x = 3.

You should be able to finish the rest following my steps.