3x+5/x=8

Solution for 3x+5/x=8 equation:

3x+5/x=8

We move all terms to the left:

3x+5/x-(8)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-8*x+5=0

We add all the numbers together, and all the variables

-8x+3x*x+5=0

Wy multiply elements

3x^2-8x+5=0

a = 3; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·3·5
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*3}=\frac{10}{6}
=1+2/3
$