100=x(21+x)

Solution for 100=x(21+x) equation:

100=x(21+x)

We move all terms to the left:

100-(x(21+x))=0

We add all the numbers together, and all the variables

-(x(x+21))+100=0


We calculate terms in parentheses: -(x(x+21)), so:

x(x+21)

We multiply parentheses

x^2+21x

Back to the equation:

-(x^2+21x)


We get rid of parentheses

-x^2-21x+100=0

We add all the numbers together, and all the variables

-1x^2-21x+100=0

a = -1; b = -21; c = +100;
Δ = b2-4ac
Δ = -212-4·(-1)·100
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-29}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+29}{2*-1}=\frac{50}{-2}
=-25
$