5x-1/10x=2

Solution for 5x-1/10x=2 equation:

5x-1/10x=2

We move all terms to the left:

5x-1/10x-(2)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


5x*10x-2*10x-1=0

Wy multiply elements

50x^2-20x-1=0

a = 50; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·50·(-1)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{6}}{2*50}=\frac{20-10\sqrt{6}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{6}}{2*50}=\frac{20+10\sqrt{6}}{100}
$