Determine the roots of x^2+12x-6=7x. What does "determine the roots" even mean?

In a quadratic equation, that is an equation in which the
variable is squared, the solutions for the values of the variable are called roots of
the equation.For example consider the equation below:

ax^2
+ bx + c = 0

In this equation x is the variable. The
quantities represented by a, b and c are known
constants.

This term root is used because the to get the
value of x we need to find the value of square root of x^2. As square root of x^2 can be
either +x, or -x, typically a quadratic equation has two
roots.

We can find the root of the given equation by first
taking all the terms of the equation on the left hand side and factorising this
expression, and then equating each factor to
0.

Thus:

x^2 + 12x - 6 =
7x

==> x^2 + 12x - 7x - 6 =
0

==> x^2 + 5x - 6 =
0

==> x^2 + 6x - x - 6 =
0

==> x(x + 6)- (x + 6) =
0

==> (x + 6)(x - 1) =
0

Therefore:

x = - 6 and
1

Thus roots of give equation are -6, and
1