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5x^2+8x+3=0

5x^2+8x+3=0 equation

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Numerical solution:

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The solution

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5*x  + 8*x + 3 = 0
(5x2+8x)+3=0\left(5 x^{2} + 8 x\right) + 3 = 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=5a = 5
b=8b = 8
c=3c = 3
, then
D = b^2 - 4 * a * c = 

(8)^2 - 4 * (5) * (3) = 4

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

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

or
x1=−35x_{1} = - \frac{3}{5}
x2=−1x_{2} = -1
Vieta's Theorem
rewrite the equation
(5x2+8x)+3=0\left(5 x^{2} + 8 x\right) + 3 = 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+8x5+35=0x^{2} + \frac{8 x}{5} + \frac{3}{5} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=85p = \frac{8}{5}
q=caq = \frac{c}{a}
q=35q = \frac{3}{5}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−85x_{1} + x_{2} = - \frac{8}{5}
x1x2=35x_{1} x_{2} = \frac{3}{5}
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.5-5001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1 - 3/5
−1−35-1 - \frac{3}{5} 
=
-8/5
−85- \frac{8}{5} 
product
-(-3) 
------
  5
−−35- \frac{-3}{5} 
=
3/5
35\frac{3}{5} 
3/5
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1 
x2 = -3/5
x2=−35x_{2} = - \frac{3}{5} 
x2 = -3/5
Numerical answer [src] 
x1 = -0.6
x2 = -1.0
x2 = -1.0
The graph
5x^2+8x+3=0 equation
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