2x+10/x=30

Solution for 2x+10/x=30 equation:

2x+10/x=30

We move all terms to the left:

2x+10/x-(30)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-30*x+10=0

We add all the numbers together, and all the variables

-30x+2x*x+10=0

Wy multiply elements

2x^2-30x+10=0

a = 2; b = -30; c = +10;
Δ = b2-4ac
Δ = -302-4·2·10
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{205}}{2*2}=\frac{30-2\sqrt{205}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{205}}{2*2}=\frac{30+2\sqrt{205}}{4}
$