x-1/20x=10

Solution for x-1/20x=10 equation:

x-1/20x=10

We move all terms to the left:

x-1/20x-(10)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We multiply all the terms by the denominator


x*20x-10*20x-1=0

Wy multiply elements

20x^2-200x-1=0

a = 20; b = -200; c = -1;
Δ = b2-4ac
Δ = -2002-4·20·(-1)
Δ = 40080
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:

$\sqrt{\Delta}=\sqrt{40080}=\sqrt{16*2505}=\sqrt{16}*\sqrt{2505}=4\sqrt{2505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2505}}{2*20}=\frac{200-4\sqrt{2505}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2505}}{2*20}=\frac{200+4\sqrt{2505}}{40}
$