x+16/100x=16.40

Solution for x+16/100x=16.40 equation:

x+16/100x=16.40

We move all terms to the left:

x+16/100x-(16.40)=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+16/100x-(16.4)=0

We add all the numbers together, and all the variables

x+16/100x-16.4=0

We multiply all the terms by the denominator


x*100x-(16.4)*100x+16=0

We multiply parentheses

x*100x-1640x+16=0

Wy multiply elements

100x^2-1640x+16=0

a = 100; b = -1640; c = +16;
Δ = b2-4ac
Δ = -16402-4·100·16
Δ = 2683200
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:

$\sqrt{\Delta}=\sqrt{2683200}=\sqrt{1600*1677}=\sqrt{1600}*\sqrt{1677}=40\sqrt{1677}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1640)-40\sqrt{1677}}{2*100}=\frac{1640-40\sqrt{1677}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1640)+40\sqrt{1677}}{2*100}=\frac{1640+40\sqrt{1677}}{200}
$