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x^2-15=2x

x^2-15=2x equation

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Numerical solution:

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The solution

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 2           
x  - 15 = 2*x
$$x^{2} - 15 = 2 x$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$x^{2} - 15 = 2 x$$
to
$$- 2 x + \left(x^{2} - 15\right) = 0$$
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -2$$
$$c = -15$$
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (1) * (-15) = 64

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 5$$
$$x_{2} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -15$$
The graph
Rapid solution [src]
x1 = -3
$$x_{1} = -3$$
x2 = 5
$$x_{2} = 5$$
x2 = 5
Sum and product of roots [src]
sum
-3 + 5
$$-3 + 5$$
=
2
$$2$$
product
-3*5
$$- 15$$
=
-15
$$-15$$
-15
Numerical answer [src]
x1 = -3.0
x2 = 5.0
x2 = 5.0
The graph
x^2-15=2x equation