x=1500+20/100x

Solution for x=1500+20/100x equation:

x=1500+20/100x

We move all terms to the left:

x-(1500+20/100x)=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-(20/100x+1500)=0

We get rid of parentheses

x-20/100x-1500=0

We multiply all the terms by the denominator


x*100x-1500*100x-20=0

Wy multiply elements

100x^2-150000x-20=0

a = 100; b = -150000; c = -20;
Δ = b2-4ac
Δ = -1500002-4·100·(-20)
Δ = 22500008000
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:

$\sqrt{\Delta}=\sqrt{22500008000}=\sqrt{1600*14062505}=\sqrt{1600}*\sqrt{14062505}=40\sqrt{14062505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150000)-40\sqrt{14062505}}{2*100}=\frac{150000-40\sqrt{14062505}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150000)+40\sqrt{14062505}}{2*100}=\frac{150000+40\sqrt{14062505}}{200}
$