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25x+4x^2-3=17+9x

25x+4x^2-3=17+9x equation

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Numerical solution:

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The solution

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25*x + 4*x  - 3 = 17 + 9*x
(4x2+25x)−3=9x+17\left(4 x^{2} + 25 x\right) - 3 = 9 x + 17
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
(4x2+25x)−3=9x+17\left(4 x^{2} + 25 x\right) - 3 = 9 x + 17
to
(−9x−17)+((4x2+25x)−3)=0\left(- 9 x - 17\right) + \left(\left(4 x^{2} + 25 x\right) - 3\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=4a = 4
b=16b = 16
c=−20c = -20
, then
D = b^2 - 4 * a * c = 

(16)^2 - 4 * (4) * (-20) = 576

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=−5x_{2} = -5
Vieta's Theorem
rewrite the equation
(4x2+25x)−3=9x+17\left(4 x^{2} + 25 x\right) - 3 = 9 x + 17
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+4x−5=0x^{2} + 4 x - 5 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=4p = 4
q=caq = \frac{c}{a}
q=−5q = -5
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−4x_{1} + x_{2} = -4
x1x2=−5x_{1} x_{2} = -5
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.0-10001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-5 + 1
−5+1-5 + 1 
=
-4
−4-4 
product
-5
−5-5 
=
-5
−5-5 
-5
Rapid solution [src] 
x1 = -5
x1=−5x_{1} = -5 
x2 = 1
x2=1x_{2} = 1 
x2 = 1
Numerical answer [src] 
x1 = 1.0
x2 = -5.0
x2 = -5.0
The graph
25x+4x^2-3=17+9x equation
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