10/x+3x=20

Solution for 10/x+3x=20 equation:

10/x+3x=20

We move all terms to the left:

10/x+3x-(20)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+10/x-20=0

We multiply all the terms by the denominator


3x*x-20*x+10=0

We add all the numbers together, and all the variables

-20x+3x*x+10=0

Wy multiply elements

3x^2-20x+10=0

a = 3; b = -20; c = +10;
Δ = b2-4ac
Δ = -202-4·3·10
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{70}}{2*3}=\frac{20-2\sqrt{70}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{70}}{2*3}=\frac{20+2\sqrt{70}}{6}
$