x-10/100x=90

Solution for x-10/100x=90 equation:

x-10/100x=90

We move all terms to the left:

x-10/100x-(90)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-90*100x-10=0

Wy multiply elements

100x^2-9000x-10=0

a = 100; b = -9000; c = -10;
Δ = b2-4ac
Δ = -90002-4·100·(-10)
Δ = 81004000
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:

$\sqrt{\Delta}=\sqrt{81004000}=\sqrt{400*202510}=\sqrt{400}*\sqrt{202510}=20\sqrt{202510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9000)-20\sqrt{202510}}{2*100}=\frac{9000-20\sqrt{202510}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9000)+20\sqrt{202510}}{2*100}=\frac{9000+20\sqrt{202510}}{200}
$