X-4=120/y

Solution for X-4=120/y equation:

X-4=120/X

We move all terms to the left:

X-4-(120/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-(+120/X)-4=0

We get rid of parentheses

X-120/X-4=0

We multiply all the terms by the denominator


X*X-4*X-120=0

We add all the numbers together, and all the variables

-4X+X*X-120=0

Wy multiply elements

X^2-4X-120=0

a = 1; b = -4; c = -120;
Δ = b2-4ac
Δ = -42-4·1·(-120)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{31}}{2*1}=\frac{4-4\sqrt{31}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{31}}{2*1}=\frac{4+4\sqrt{31}}{2}
$