x-8/x+2=x-1/2x+10

Solution for x-8/x+2=x-1/2x+10 equation:

x-8/x+2=x-1/2x+10

We move all terms to the left:

x-8/x+2-(x-1/2x+10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+10)!=0

x∈R


We get rid of parentheses

x-8/x-x+1/2x-10+2=0

We calculate fractions


x-x+(-16x)/2x^2+x/2x^2-10+2=0

We add all the numbers together, and all the variables

(-16x)/2x^2+x/2x^2-8=0

We multiply all the terms by the denominator


(-16x)+x-8*2x^2=0

We add all the numbers together, and all the variables

x+(-16x)-8*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-16x^2-15x=0

a = -16; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-16)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-16}=\frac{30}{-32}
=-15/16
$