x^2/(x+2)=625

Solution for x^2/(x+2)=625 equation:

x^2/(x+2)=625

We move all terms to the left:

x^2/(x+2)-(625)=0


Domain of the equation: (x+2)!=0

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

x!=-2

x∈R


We multiply all the terms by the denominator


x^2-625*(x+2)=0

We multiply parentheses

x^2-625x-1250=0

a = 1; b = -625; c = -1250;
Δ = b2-4ac
Δ = -6252-4·1·(-1250)
Δ = 395625
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:

$\sqrt{\Delta}=\sqrt{395625}=\sqrt{625*633}=\sqrt{625}*\sqrt{633}=25\sqrt{633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-625)-25\sqrt{633}}{2*1}=\frac{625-25\sqrt{633}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-625)+25\sqrt{633}}{2*1}=\frac{625+25\sqrt{633}}{2}
$