x-4/10x=500

Solution for x-4/10x=500 equation:

x-4/10x=500

We move all terms to the left:

x-4/10x-(500)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


x*10x-500*10x-4=0

Wy multiply elements

10x^2-5000x-4=0

a = 10; b = -5000; c = -4;
Δ = b2-4ac
Δ = -50002-4·10·(-4)
Δ = 25000160
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:

$\sqrt{\Delta}=\sqrt{25000160}=\sqrt{16*1562510}=\sqrt{16}*\sqrt{1562510}=4\sqrt{1562510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5000)-4\sqrt{1562510}}{2*10}=\frac{5000-4\sqrt{1562510}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5000)+4\sqrt{1562510}}{2*10}=\frac{5000+4\sqrt{1562510}}{20}
$