X+5/y=8

Solution for X+5/y=8 equation:

X+5/X=8

We move all terms to the left:

X+5/X-(8)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-8*X+5=0

We add all the numbers together, and all the variables

-8X+X*X+5=0

Wy multiply elements

X^2-8X+5=0

a = 1; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·1·5
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{11}}{2*1}=\frac{8-2\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{11}}{2*1}=\frac{8+2\sqrt{11}}{2}
$