2x-10=30/x

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

2x-10=30/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-30/x-10=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2-10x-30=0

a = 2; b = -10; c = -30;
Δ = b2-4ac
Δ = -102-4·2·(-30)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*2}=\frac{10-2\sqrt{85}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*2}=\frac{10+2\sqrt{85}}{4}
$