x-3/10x=100

Solution for x-3/10x=100 equation:

x-3/10x=100

We move all terms to the left:

x-3/10x-(100)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


x*10x-100*10x-3=0

Wy multiply elements

10x^2-1000x-3=0

a = 10; b = -1000; c = -3;
Δ = b2-4ac
Δ = -10002-4·10·(-3)
Δ = 1000120
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:

$\sqrt{\Delta}=\sqrt{1000120}=\sqrt{4*250030}=\sqrt{4}*\sqrt{250030}=2\sqrt{250030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-2\sqrt{250030}}{2*10}=\frac{1000-2\sqrt{250030}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+2\sqrt{250030}}{2*10}=\frac{1000+2\sqrt{250030}}{20}
$