X-5/x=2x-10/x+8

Solution for X-5/x=2x-10/x+8 equation:

X-5/X=2X-10/X+8

We move all terms to the left:

X-5/X-(2X-10/X+8)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X+8)!=0

X∈R


We get rid of parentheses

X-5/X-2X+10/X-8=0

We multiply all the terms by the denominator


X*X-2X*X-8*X-5+10=0

We add all the numbers together, and all the variables

-8X+X*X-2X*X+5=0

Wy multiply elements

X^2-2X^2-8X+5=0

We add all the numbers together, and all the variables

-1X^2-8X+5=0

a = -1; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·(-1)·5
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{21}}{2*-1}=\frac{8-2\sqrt{21}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{21}}{2*-1}=\frac{8+2\sqrt{21}}{-2}
$