X-16/100x=21.84

Solution for X-16/100x=21.84 equation:

X-16/100X=21.84

We move all terms to the left:

X-16/100X-(21.84)=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-21.84=0

We multiply all the terms by the denominator


X*100X-(21.84)*100X-16=0

We multiply parentheses

X*100X-2184X-16=0

Wy multiply elements

100X^2-2184X-16=0

a = 100; b = -2184; c = -16;
Δ = b2-4ac
Δ = -21842-4·100·(-16)
Δ = 4776256
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:

$\sqrt{\Delta}=\sqrt{4776256}=\sqrt{64*74629}=\sqrt{64}*\sqrt{74629}=8\sqrt{74629}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2184)-8\sqrt{74629}}{2*100}=\frac{2184-8\sqrt{74629}}{200}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2184)+8\sqrt{74629}}{2*100}=\frac{2184+8\sqrt{74629}}{200}
$