x+12/100x=16.80

Solution for x+12/100x=16.80 equation:

x+12/100x=16.80

We move all terms to the left:

x+12/100x-(16.80)=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+12/100x-(16.8)=0

We add all the numbers together, and all the variables

x+12/100x-16.8=0

We multiply all the terms by the denominator


x*100x-(16.8)*100x+12=0

We multiply parentheses

x*100x-1680x+12=0

Wy multiply elements

100x^2-1680x+12=0

a = 100; b = -1680; c = +12;
Δ = b2-4ac
Δ = -16802-4·100·12
Δ = 2817600
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:

$\sqrt{\Delta}=\sqrt{2817600}=\sqrt{1600*1761}=\sqrt{1600}*\sqrt{1761}=40\sqrt{1761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1680)-40\sqrt{1761}}{2*100}=\frac{1680-40\sqrt{1761}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1680)+40\sqrt{1761}}{2*100}=\frac{1680+40\sqrt{1761}}{200}
$