((x^2-150x+15000)/x)=100

Solution for ((x^2-150x+15000)/x)=100 equation:

((x^2-150x+15000)/x)=100

We move all terms to the left:

((x^2-150x+15000)/x)-(100)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


((x^2-150x+15000)-100*x)=0


We calculate terms in parentheses: +((x^2-150x+15000)-100*x), so:

(x^2-150x+15000)-100*x

We add all the numbers together, and all the variables

-100x+(x^2-150x+15000)

We get rid of parentheses

x^2-100x-150x+15000

We add all the numbers together, and all the variables

x^2-250x+15000

Back to the equation:

+(x^2-250x+15000)


We get rid of parentheses

x^2-250x+15000=0

a = 1; b = -250; c = +15000;
Δ = b2-4ac
Δ = -2502-4·1·15000
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-50}{2*1}=\frac{200}{2}
=100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+50}{2*1}=\frac{300}{2}
=150
$