x(2+x)=0.21

Solution for x(2+x)=0.21 equation:

x(2+x)=0.21

We move all terms to the left:

x(2+x)-(0.21)=0

We add all the numbers together, and all the variables

x(x+2)-(0.21)=0

We add all the numbers together, and all the variables

x(x+2)-0.21=0

We multiply parentheses

x^2+2x-0.21=0

a = 1; b = 2; c = -0.21;
Δ = b2-4ac
Δ = 22-4·1·(-0.21)
Δ = 4.84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-\sqrt{4.84}}{2*1}=\frac{-2-\sqrt{4.84}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{4.84}}{2*1}=\frac{-2+\sqrt{4.84}}{2}
$