(x^2)/(x+10)=50

Solution for (x^2)/(x+10)=50 equation:

(x^2)/(x+10)=50

We move all terms to the left:

(x^2)/(x+10)-(50)=0


Domain of the equation: (x+10)!=0

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

x!=-10

x∈R


We multiply all the terms by the denominator


x^2-50*(x+10)=0

We multiply parentheses

x^2-50x-500=0

a = 1; b = -50; c = -500;
Δ = b2-4ac
Δ = -502-4·1·(-500)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-30\sqrt{5}}{2*1}=\frac{50-30\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+30\sqrt{5}}{2*1}=\frac{50+30\sqrt{5}}{2}
$