x+3/20x=2

Solution for x+3/20x=2 equation:

x+3/20x=2

We move all terms to the left:

x+3/20x-(2)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We multiply all the terms by the denominator


x*20x-2*20x+3=0

Wy multiply elements

20x^2-40x+3=0

a = 20; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·20·3
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{85}}{2*20}=\frac{40-4\sqrt{85}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{85}}{2*20}=\frac{40+4\sqrt{85}}{40}
$