99/100(x)+x=1000

Solution for 99/100(x)+x=1000 equation:

99/100(x)+x=1000

We move all terms to the left:

99/100(x)+x-(1000)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We add all the numbers together, and all the variables

x+99/100x-1000=0

We multiply all the terms by the denominator


x*100x-1000*100x+99=0

Wy multiply elements

100x^2-100000x+99=0

a = 100; b = -100000; c = +99;
Δ = b2-4ac
Δ = -1000002-4·100·99
Δ = 9999960400
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:

$\sqrt{\Delta}=\sqrt{9999960400}=\sqrt{400*24999901}=\sqrt{400}*\sqrt{24999901}=20\sqrt{24999901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100000)-20\sqrt{24999901}}{2*100}=\frac{100000-20\sqrt{24999901}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100000)+20\sqrt{24999901}}{2*100}=\frac{100000+20\sqrt{24999901}}{200}
$