100=(X^2+2500)/(2*x)

Solution for 100=(X^2+2500)/(2*x) equation:

100=(X^2+2500)/(2X)

We move all terms to the left:

100-((X^2+2500)/(2X))=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We multiply all the terms by the denominator


-((X^2+2500)+100*2X)=0


We calculate terms in parentheses: -((X^2+2500)+100*2X), so:

(X^2+2500)+100*2X

Wy multiply elements

(X^2+2500)+200X

We get rid of parentheses

X^2+200X+2500

Back to the equation:

-(X^2+200X+2500)


We get rid of parentheses

-X^2-200X-2500=0

We add all the numbers together, and all the variables

-1X^2-200X-2500=0

a = -1; b = -200; c = -2500;
Δ = b2-4ac
Δ = -2002-4·(-1)·(-2500)
Δ = 30000
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:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-100\sqrt{3}}{2*-1}=\frac{200-100\sqrt{3}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+100\sqrt{3}}{2*-1}=\frac{200+100\sqrt{3}}{-2}
$