5^5=x^2/(x+3)

Solution for 5^5=x^2/(x+3) equation:

5^5=x^2/(x+3)

We move all terms to the left:

5^5-(x^2/(x+3))=0


Domain of the equation: (x+3))!=0

x∈R


We add all the numbers together, and all the variables

-(x^2/(x+3))+3125=0

We multiply all the terms by the denominator


-(x^2+3125*(x+3))=0


We calculate terms in parentheses: -(x^2+3125*(x+3)), so:

x^2+3125*(x+3)

We multiply parentheses

x^2+3125x+9375

Back to the equation:

-(x^2+3125x+9375)


We get rid of parentheses

-x^2-3125x-9375=0

We add all the numbers together, and all the variables

-1x^2-3125x-9375=0

a = -1; b = -3125; c = -9375;
Δ = b2-4ac
Δ = -31252-4·(-1)·(-9375)
Δ = 9728125
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:

$\sqrt{\Delta}=\sqrt{9728125}=\sqrt{625*15565}=\sqrt{625}*\sqrt{15565}=25\sqrt{15565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3125)-25\sqrt{15565}}{2*-1}=\frac{3125-25\sqrt{15565}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3125)+25\sqrt{15565}}{2*-1}=\frac{3125+25\sqrt{15565}}{-2}
$