5*a(2+a)=20

Solution for 5*a(2+a)=20 equation:

5a(2+a)=20

We move all terms to the left:

5a(2+a)-(20)=0

We add all the numbers together, and all the variables

5a(a+2)-20=0

We multiply parentheses

5a^2+10a-20=0

a = 5; b = 10; c = -20;
Δ = b2-4ac
Δ = 102-4·5·(-20)
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{5}}{2*5}=\frac{-10-10\sqrt{5}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{5}}{2*5}=\frac{-10+10\sqrt{5}}{10}
$