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7+5x-2x^2=0

7+5x-2x^2=0 equation

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Numerical solution:

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The solution

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7 + 5*x - 2*x  = 0
−2x2+(5x+7)=0- 2 x^{2} + \left(5 x + 7\right) = 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=−2a = -2
b=5b = 5
c=7c = 7
, then
D = b^2 - 4 * a * c = 

(5)^2 - 4 * (-2) * (7) = 81

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

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

or
x1=−1x_{1} = -1
x2=72x_{2} = \frac{7}{2}
Vieta's Theorem
rewrite the equation
−2x2+(5x+7)=0- 2 x^{2} + \left(5 x + 7\right) = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−5x2−72=0x^{2} - \frac{5 x}{2} - \frac{7}{2} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−52p = - \frac{5}{2}
q=caq = \frac{c}{a}
q=−72q = - \frac{7}{2}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=52x_{1} + x_{2} = \frac{5}{2}
x1x2=−72x_{1} x_{2} = - \frac{7}{2}
The graph
05-15-10-5101520-500500
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1 + 7/2
−1+72-1 + \frac{7}{2} 
=
5/2
52\frac{5}{2} 
product
-7 
---
 2
−72- \frac{7}{2} 
=
-7/2
−72- \frac{7}{2} 
-7/2
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1 
x2 = 7/2
x2=72x_{2} = \frac{7}{2} 
x2 = 7/2
Numerical answer [src] 
x1 = 3.5
x2 = -1.0
x2 = -1.0
The graph
7+5x-2x^2=0 equation
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