(x^2)/(x+20)-10=0

Solution for (x^2)/(x+20)-10=0 equation:

(x^2)/(x+20)-10=0


Domain of the equation: (x+20)!=0

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

x!=-20

x∈R


We multiply all the terms by the denominator


x^2-10*(x+20)=0

We multiply parentheses

x^2-10x-200=0

a = 1; b = -10; c = -200;
Δ = b2-4ac
Δ = -102-4·1·(-200)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*1}=\frac{40}{2}
=20
$