x+16/100x=19.72

Solution for x+16/100x=19.72 equation:

x+16/100x=19.72

We move all terms to the left:

x+16/100x-(19.72)=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-19.72=0

We multiply all the terms by the denominator


x*100x-(19.72)*100x+16=0

We multiply parentheses

x*100x-1972x+16=0

Wy multiply elements

100x^2-1972x+16=0

a = 100; b = -1972; c = +16;
Δ = b2-4ac
Δ = -19722-4·100·16
Δ = 3882384
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:

$\sqrt{\Delta}=\sqrt{3882384}=\sqrt{144*26961}=\sqrt{144}*\sqrt{26961}=12\sqrt{26961}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1972)-12\sqrt{26961}}{2*100}=\frac{1972-12\sqrt{26961}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1972)+12\sqrt{26961}}{2*100}=\frac{1972+12\sqrt{26961}}{200}
$