X+y=220.X/y=4y

Solution for X+y=220.X/y=4y equation:

X+X=220.X/X=4X

We move all terms to the left:

X+X-(220.X/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+X-(+220.X/X)=0

We add all the numbers together, and all the variables

2X-(+220.X/X)=0

We get rid of parentheses

2X-220.X/X=0

We multiply all the terms by the denominator


2X*X-220.X=0

We add all the numbers together, and all the variables

-220X+2X*X=0

Wy multiply elements

2X^2-220X=0

a = 2; b = -220; c = 0;
Δ = b2-4ac
Δ = -2202-4·2·0
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-220}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+220}{2*2}=\frac{440}{4}
=110
$