10/x-2x-8=0

Solution for 10/x-2x-8=0 equation:

10/x-2x-8=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+10/x-8=0

We multiply all the terms by the denominator


-2x*x-8*x+10=0

We add all the numbers together, and all the variables

-8x-2x*x+10=0

Wy multiply elements

-2x^2-8x+10=0

a = -2; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·(-2)·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*-2}=\frac{20}{-4}
=-5
$