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x^2+3*x-10=0

x^2+3*x-10=0 equation

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Numerical solution:

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The solution

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 2               
x  + 3*x - 10 = 0
(x2+3x)−10=0\left(x^{2} + 3 x\right) - 10 = 0
Simplify
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:
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=1a = 1
b=3b = 3
c=−10c = -10
, then
D = b^2 - 4 * a * c = 

(3)^2 - 4 * (1) * (-10) = 49

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

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

or
x1=2x_{1} = 2
x2=−5x_{2} = -5
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=3p = 3
q=caq = \frac{c}{a}
q=−10q = -10
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−3x_{1} + x_{2} = -3
x1x2=−10x_{1} x_{2} = -10
The graph
05-20-15-10-51015-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -5
x1=−5x_{1} = -5 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Sum and product of roots [src] 
sum
-5 + 2
−5+2-5 + 2 
=
-3
−3-3 
product
-5*2
−10- 10 
=
-10
−10-10 
-10
Numerical answer [src] 
x1 = 2.0
x2 = -5.0
x2 = -5.0
The graph
x^2+3*x-10=0 equation
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