(2(8-3x))/x=x

Solution for (2(8-3x))/x=x equation:

(2(8-3x))/x=x

We move all terms to the left:

(2(8-3x))/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(2(-3x+8))/x-x=0

We add all the numbers together, and all the variables

-1x+(2(-3x+8))/x=0

We multiply all the terms by the denominator


-1x*x+(2(-3x+8))=0


We calculate terms in parentheses: +(2(-3x+8)), so:

2(-3x+8)

We multiply parentheses

-6x+16

Back to the equation:

+(-6x+16)


Wy multiply elements

-1x^2+(-6x+16)=0

We get rid of parentheses

-1x^2-6x+16=0

a = -1; b = -6; c = +16;
Δ = b2-4ac
Δ = -62-4·(-1)·16
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-1}=\frac{16}{-2}
=-8
$