x=200+7/100x

Solution for x=200+7/100x equation:

x=200+7/100x

We move all terms to the left:

x-(200+7/100x)=0


Domain of the equation: 100x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(7/100x+200)=0

We get rid of parentheses

x-7/100x-200=0

We multiply all the terms by the denominator


x*100x-200*100x-7=0

Wy multiply elements

100x^2-20000x-7=0

a = 100; b = -20000; c = -7;
Δ = b2-4ac
Δ = -200002-4·100·(-7)
Δ = 400002800
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:

$\sqrt{\Delta}=\sqrt{400002800}=\sqrt{400*1000007}=\sqrt{400}*\sqrt{1000007}=20\sqrt{1000007}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20000)-20\sqrt{1000007}}{2*100}=\frac{20000-20\sqrt{1000007}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20000)+20\sqrt{1000007}}{2*100}=\frac{20000+20\sqrt{1000007}}{200}
$