225=(x)(8+x)

Solution for 225=(x)(8+x) equation:

225=(x)(8+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x(x+8))+225=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+225=0

We add all the numbers together, and all the variables

-1x^2-8x+225=0

a = -1; b = -8; c = +225;
Δ = b2-4ac
Δ = -82-4·(-1)·225
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{241}}{2*-1}=\frac{8-2\sqrt{241}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{241}}{2*-1}=\frac{8+2\sqrt{241}}{-2}
$