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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-5x^2+20x-(-5x+20)=0

We get rid of parentheses

-5x^2+20x+5x-20=0

We add all the numbers together, and all the variables

-5x^2+25x-20=0

a = -5; b = 25; c = -20;
Δ = b2-4ac
Δ = 252-4·(-5)·(-20)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15}{2*-5}=\frac{-40}{-10}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15}{2*-5}=\frac{-10}{-10}
=1
$