3/100*x=169.95-x

Solution for 3/100*x=169.95-x equation:

3/100x=169.95-x

We move all terms to the left:

3/100x-(169.95-x)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We add all the numbers together, and all the variables

3/100x-(-1x+169.95)=0

We get rid of parentheses

3/100x+1x-169.95=0

We multiply all the terms by the denominator


1x*100x-(169.95)*100x+3=0

We multiply parentheses

1x*100x-16995x+3=0

Wy multiply elements

100x^2-16995x+3=0

a = 100; b = -16995; c = +3;
Δ = b2-4ac
Δ = -169952-4·100·3
Δ = 288828825
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:

$\sqrt{\Delta}=\sqrt{288828825}=\sqrt{25*11553153}=\sqrt{25}*\sqrt{11553153}=5\sqrt{11553153}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16995)-5\sqrt{11553153}}{2*100}=\frac{16995-5\sqrt{11553153}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16995)+5\sqrt{11553153}}{2*100}=\frac{16995+5\sqrt{11553153}}{200}
$