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(6x-24)*(x+19)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
(6*x - 24)*(x + 19) = 0
(x+19)(6x−24)=0\left(x + 19\right) \left(6 x - 24\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(x+19)(6x−24)=0\left(x + 19\right) \left(6 x - 24\right) = 0
We get the quadratic equation
6x2+90x−456=06 x^{2} + 90 x - 456 = 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=6a = 6
b=90b = 90
c=−456c = -456
, then
D = b^2 - 4 * a * c = 

(90)^2 - 4 * (6) * (-456) = 19044

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

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

or
x1=4x_{1} = 4
x2=−19x_{2} = -19
Sum and product of roots [src] 
sum
-19 + 4
−19+4-19 + 4 
=
-15
−15-15 
product
-19*4
−76- 76 
=
-76
−76-76 
-76
Rapid solution [src] 
x1 = -19
x1=−19x_{1} = -19 
x2 = 4
x2=4x_{2} = 4 
x2 = 4
Numerical answer [src] 
x1 = -19.0
x2 = 4.0
x2 = 4.0
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