3x+8/x=10

Solution for 3x+8/x=10 equation:

3x+8/x=10

We move all terms to the left:

3x+8/x-(10)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-10*x+8=0

We add all the numbers together, and all the variables

-10x+3x*x+8=0

Wy multiply elements

3x^2-10x+8=0

a = 3; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·3·8
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{-(-10)-2}{2*3}=\frac{8}{6}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*3}=\frac{12}{6}
=2
$