180=2x+x(x+8)

Solution for 180=2x+x(x+8) equation:

180=2x+x(x+8)

We move all terms to the left:

180-(2x+x(x+8))=0


We calculate terms in parentheses: -(2x+x(x+8)), so:

2x+x(x+8)

We multiply parentheses

x^2+2x+8x

We add all the numbers together, and all the variables

x^2+10x

Back to the equation:

-(x^2+10x)


We get rid of parentheses

-x^2-10x+180=0

We add all the numbers together, and all the variables

-1x^2-10x+180=0

a = -1; b = -10; c = +180;
Δ = b2-4ac
Δ = -102-4·(-1)·180
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{205}}{2*-1}=\frac{10-2\sqrt{205}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{205}}{2*-1}=\frac{10+2\sqrt{205}}{-2}
$