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4*x^2-25=0

4*x^2-25=0 equation

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Numerical solution:

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The solution

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4*x  - 25 = 0
$$4 x^{2} - 25 = 0$$
Detail solution
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
$$a = 4$$
$$b = 0$$
$$c = -25$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (4) * (-25) = 400

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

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

or
$$x_{1} = \frac{5}{2}$$
$$x_{2} = - \frac{5}{2}$$
Vieta's Theorem
rewrite the equation
$$4 x^{2} - 25 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{25}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{25}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{25}{4}$$
The graph
Rapid solution [src]
x1 = -5/2
$$x_{1} = - \frac{5}{2}$$
x2 = 5/2
$$x_{2} = \frac{5}{2}$$
x2 = 5/2
Sum and product of roots [src]
sum
-5/2 + 5/2
$$- \frac{5}{2} + \frac{5}{2}$$
=
0
$$0$$
product
-5*5
----
2*2 
$$- \frac{25}{4}$$
=
-25/4
$$- \frac{25}{4}$$
-25/4
Numerical answer [src]
x1 = -2.5
x2 = 2.5
x2 = 2.5
The graph
4*x^2-25=0 equation