X=16-1/20y

Solution for X=16-1/20y equation:

X=16-1/20X

We move all terms to the left:

X-(16-1/20X)=0


Domain of the equation: 20X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(-1/20X+16)=0

We get rid of parentheses

X+1/20X-16=0

We multiply all the terms by the denominator


X*20X-16*20X+1=0

Wy multiply elements

20X^2-320X+1=0

a = 20; b = -320; c = +1;
Δ = b2-4ac
Δ = -3202-4·20·1
Δ = 102320
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:

$\sqrt{\Delta}=\sqrt{102320}=\sqrt{16*6395}=\sqrt{16}*\sqrt{6395}=4\sqrt{6395}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-4\sqrt{6395}}{2*20}=\frac{320-4\sqrt{6395}}{40}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+4\sqrt{6395}}{2*20}=\frac{320+4\sqrt{6395}}{40}
$