10000=x*x+(x+20)(x+20)

Solution for 10000=x*x+(x+20)(x+20) equation:

10000=x*x+(x+20)(x+20)

We move all terms to the left:

10000-(x*x+(x+20)(x+20))=0

We multiply parentheses ..

-(x*x+(+x^2+20x+20x+400))+10000=0


We calculate terms in parentheses: -(x*x+(+x^2+20x+20x+400)), so:

x*x+(+x^2+20x+20x+400)

determiningTheFunctionDomain
(+x^2+20x+20x+400)+x*x

Wy multiply elements

(+x^2+20x+20x+400)+x^2

We get rid of parentheses

x^2+x^2+20x+20x+400

We add all the numbers together, and all the variables

2x^2+40x+400

Back to the equation:

-(2x^2+40x+400)


We get rid of parentheses

-2x^2-40x-400+10000=0

We add all the numbers together, and all the variables

-2x^2-40x+9600=0

a = -2; b = -40; c = +9600;
Δ = b2-4ac
Δ = -402-4·(-2)·9600
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-280}{2*-2}=\frac{-240}{-4}
=+60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+280}{2*-2}=\frac{320}{-4}
=-80
$