x=8/x+3

Solution for x=8/x+3 equation:

x=8/x+3

We move all terms to the left:

x-(8/x+3)=0


Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

x-8/x-3=0

We multiply all the terms by the denominator


x*x-3*x-8=0

We add all the numbers together, and all the variables

-3x+x*x-8=0

Wy multiply elements

x^2-3x-8=0

a = 1; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·1·(-8)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{41}}{2*1}=\frac{3-\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*1}=\frac{3+\sqrt{41}}{2}
$