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2x*(3+8x)-(4x-3)*(4x+3)=1,5x equation

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Numerical solution:

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The solution

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                                      3*x
2*x*(3 + 8*x) - (4*x - 3)*(4*x + 3) = ---
                                       2 
$$2 x \left(8 x + 3\right) - \left(4 x - 3\right) \left(4 x + 3\right) = \frac{3 x}{2}$$
Detail solution
Given the equation:
2*x*(3+8*x)-(4*x-3)*(4*x+3) = (3/2)*x

Expand expressions:
6*x + 16*x^2 - (4*x - 3)*(4*x + 3) = (3/2)*x

6*x + 16*x^2 + 9 - 16*x^2 = (3/2)*x

2*x*(3+8*x)-(4*x-3)*(4*x+3) = 3*x/2

Reducing, you get:
9 + 9*x/2 = 0

Move free summands (without x)
from left part to right part, we given:
$$\frac{9 x}{2} = -9$$
Divide both parts of the equation by 9/2
x = -9 / (9/2)

We get the answer: x = -2
The graph
Rapid solution [src]
x1 = -2
$$x_{1} = -2$$
x1 = -2
Sum and product of roots [src]
sum
-2
$$-2$$
=
-2
$$-2$$
product
-2
$$-2$$
=
-2
$$-2$$
-2
Numerical answer [src]
x1 = -2.0
x1 = -2.0