10x-4/x=2

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

10x-4/x=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

10x^2-2x-4=0

a = 10; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·10·(-4)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{41}}{2*10}=\frac{2-2\sqrt{41}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{41}}{2*10}=\frac{2+2\sqrt{41}}{20}
$