2504^2=x(x+8)

Solution for 2504^2=x(x+8) equation:

2504^2=x(x+8)

We move all terms to the left:

2504^2-(x(x+8))=0

We add all the numbers together, and all the variables

-(x(x+8))+6270016=0


We calculate terms in parentheses: -(x(x+8)), so:

x(x+8)

We multiply parentheses

x^2+8x

Back to the equation:

-(x^2+8x)


We get rid of parentheses

-x^2-8x+6270016=0

We add all the numbers together, and all the variables

-1x^2-8x+6270016=0

a = -1; b = -8; c = +6270016;
Δ = b2-4ac
Δ = -82-4·(-1)·6270016
Δ = 25080128
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:

$\sqrt{\Delta}=\sqrt{25080128}=\sqrt{64*391877}=\sqrt{64}*\sqrt{391877}=8\sqrt{391877}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{391877}}{2*-1}=\frac{8-8\sqrt{391877}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{391877}}{2*-1}=\frac{8+8\sqrt{391877}}{-2}
$