2x=10/x-4

Solution for 2x=10/x-4 equation:

2x=10/x-4

We move all terms to the left:

2x-(10/x-4)=0


Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

2x-10/x+4=0

We multiply all the terms by the denominator


2x*x+4*x-10=0

We add all the numbers together, and all the variables

4x+2x*x-10=0

Wy multiply elements

2x^2+4x-10=0

a = 2; b = 4; c = -10;
Δ = b2-4ac
Δ = 42-4·2·(-10)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*2}=\frac{-4-4\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*2}=\frac{-4+4\sqrt{6}}{4}
$