(x^2)/(x+100)=50

Solution for (x^2)/(x+100)=50 equation:

(x^2)/(x+100)=50

We move all terms to the left:

(x^2)/(x+100)-(50)=0


Domain of the equation: (x+100)!=0

We move all terms containing x to the left, all other terms to the right

x!=-100

x∈R


We multiply all the terms by the denominator


x^2-50*(x+100)=0

We multiply parentheses

x^2-50x-5000=0

a = 1; b = -50; c = -5000;
Δ = b2-4ac
Δ = -502-4·1·(-5000)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-150}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+150}{2*1}=\frac{200}{2}
=100
$