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2x+5x^2-4=6+7x

2x+5x^2-4=6+7x equation

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Numerical solution:

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The solution

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2*x + 5*x  - 4 = 6 + 7*x
(5x2+2x)−4=7x+6\left(5 x^{2} + 2 x\right) - 4 = 7 x + 6
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
(5x2+2x)−4=7x+6\left(5 x^{2} + 2 x\right) - 4 = 7 x + 6
to
(−7x−6)+((5x2+2x)−4)=0\left(- 7 x - 6\right) + \left(\left(5 x^{2} + 2 x\right) - 4\right) = 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=−5b = -5
c=−10c = -10
, then
D = b^2 - 4 * a * c = 

(-5)^2 - 4 * (5) * (-10) = 225

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=−1x_{2} = -1
Vieta's Theorem
rewrite the equation
(5x2+2x)−4=7x+6\left(5 x^{2} + 2 x\right) - 4 = 7 x + 6
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−x−2=0x^{2} - x - 2 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−1p = -1
q=caq = \frac{c}{a}
q=−2q = -2
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=1x_{1} + x_{2} = 1
x1x2=−2x_{1} x_{2} = -2
The graph
02468-10-8-6-4-21210-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1 
x2 = 2
x2=2x_{2} = 2 
x2 = 2
Sum and product of roots [src] 
sum
-1 + 2
−1+2-1 + 2 
=
1
11 
product
-2
−2- 2 
=
-2
−2-2 
-2
Numerical answer [src] 
x1 = 2.0
x2 = -1.0
x2 = -1.0
The graph
2x+5x^2-4=6+7x equation
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