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3x^2+5x-2=0

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

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Numerical solution:

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The solution

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

(5)^2 - 4 * (3) * (-2) = 49

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

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

or
x1=13x_{1} = \frac{1}{3}
x2=−2x_{2} = -2
Vieta's Theorem
rewrite the equation
(3x2+5x)−2=0\left(3 x^{2} + 5 x\right) - 2 = 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+5x3−23=0x^{2} + \frac{5 x}{3} - \frac{2}{3} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=53p = \frac{5}{3}
q=caq = \frac{c}{a}
q=−23q = - \frac{2}{3}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−53x_{1} + x_{2} = - \frac{5}{3}
x1x2=−23x_{1} x_{2} = - \frac{2}{3}
The graph
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-2 + 1/3
−2+13-2 + \frac{1}{3} 
=
-5/3
−53- \frac{5}{3} 
product
-2 
---
 3
−23- \frac{2}{3} 
=
-2/3
−23- \frac{2}{3} 
-2/3
Rapid solution [src] 
x1 = -2
x1=−2x_{1} = -2 
x2 = 1/3
x2=13x_{2} = \frac{1}{3} 
x2 = 1/3
Numerical answer [src] 
x1 = -2.0
x2 = 0.333333333333333
x2 = 0.333333333333333
The graph
3x^2+5x-2=0 equation
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