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(x-7)(-5x-9)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
(x - 7)*(-5*x - 9) = 0
(−5x−9)(x−7)=0\left(- 5 x - 9\right) \left(x - 7\right) = 0
Simplify
Detail solution
Expand the expression in the equation
(−5x−9)(x−7)=0\left(- 5 x - 9\right) \left(x - 7\right) = 0
We get the quadratic equation
−5x2+26x+63=0- 5 x^{2} + 26 x + 63 = 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=−5a = -5
b=26b = 26
c=63c = 63
, then
D = b^2 - 4 * a * c = 

(26)^2 - 4 * (-5) * (63) = 1936

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

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

or
x1=−95x_{1} = - \frac{9}{5}
x2=7x_{2} = 7
Rapid solution [src] 
x1 = -9/5
x1=−95x_{1} = - \frac{9}{5} 
x2 = 7
x2=7x_{2} = 7 
x2 = 7
Sum and product of roots [src] 
sum
7 - 9/5
−95+7- \frac{9}{5} + 7 
=
26/5
265\frac{26}{5} 
product
7*(-9)
------
  5
(−9)75\frac{\left(-9\right) 7}{5} 
=
-63/5
−635- \frac{63}{5} 
-63/5
Numerical answer [src] 
x1 = 7.0
x2 = -1.8
x2 = -1.8
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