4x(5-x)=20

Solution for 4x(5-x)=20 equation:

4x(5-x)=20

We move all terms to the left:

4x(5-x)-(20)=0

We add all the numbers together, and all the variables

4x(-1x+5)-20=0

We multiply parentheses

-4x^2+20x-20=0

a = -4; b = 20; c = -20;
Δ = b2-4ac
Δ = 202-4·(-4)·(-20)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{5}}{2*-4}=\frac{-20-4\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{5}}{2*-4}=\frac{-20+4\sqrt{5}}{-8}
$