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

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

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

We multiply parentheses

x^2-2x-20=0

a = 1; b = -2; c = -20;
Δ = b2-4ac
Δ = -22-4·1·(-20)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*1}=\frac{2-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*1}=\frac{2+2\sqrt{21}}{2}
$