8/230*x-2=x

Solution for 8/230*x-2=x equation:

8/230x-2=x

We move all terms to the left:

8/230x-2-(x)=0


Domain of the equation: 230x!=0

x!=0/230

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8/230x-2=0

We multiply all the terms by the denominator


-1x*230x-2*230x+8=0

Wy multiply elements

-230x^2-460x+8=0

a = -230; b = -460; c = +8;
Δ = b2-4ac
Δ = -4602-4·(-230)·8
Δ = 218960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{218960}=\sqrt{16*13685}=\sqrt{16}*\sqrt{13685}=4\sqrt{13685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-4\sqrt{13685}}{2*-230}=\frac{460-4\sqrt{13685}}{-460}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+4\sqrt{13685}}{2*-230}=\frac{460+4\sqrt{13685}}{-460}
$