X=420/x

Solution for X=420/x equation:

X=420/X

We move all terms to the left:

X-(420/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-(+420/X)=0

We get rid of parentheses

X-420/X=0

We multiply all the terms by the denominator


X*X-420=0

Wy multiply elements

X^2-420=0

a = 1; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·1·(-420)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*1}=\frac{0-4\sqrt{105}}{2}
=-\frac{4\sqrt{105}}{2}
=-2\sqrt{105}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*1}=\frac{0+4\sqrt{105}}{2}
=\frac{4\sqrt{105}}{2}
=2\sqrt{105}
$