20x+3/5x=500

Solution for 20x+3/5x=500 equation:

20x+3/5x=500

We move all terms to the left:

20x+3/5x-(500)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


20x*5x-500*5x+3=0

Wy multiply elements

100x^2-2500x+3=0

a = 100; b = -2500; c = +3;
Δ = b2-4ac
Δ = -25002-4·100·3
Δ = 6248800
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:

$\sqrt{\Delta}=\sqrt{6248800}=\sqrt{400*15622}=\sqrt{400}*\sqrt{15622}=20\sqrt{15622}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2500)-20\sqrt{15622}}{2*100}=\frac{2500-20\sqrt{15622}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2500)+20\sqrt{15622}}{2*100}=\frac{2500+20\sqrt{15622}}{200}
$