0=50x(80-2x)

Solution for 0=50x(80-2x) equation:

0=50x(80-2x)

We move all terms to the left:

0-(50x(80-2x))=0

We add all the numbers together, and all the variables

-(50x(-2x+80))+0=0

We add all the numbers together, and all the variables

-(50x(-2x+80))=0


We calculate terms in parentheses: -(50x(-2x+80)), so:

50x(-2x+80)

We multiply parentheses

-100x^2+4000x

Back to the equation:

-(-100x^2+4000x)


We get rid of parentheses

100x^2-4000x=0

a = 100; b = -4000; c = 0;
Δ = b2-4ac
Δ = -40002-4·100·0
Δ = 16000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16000000}=4000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4000)-4000}{2*100}=\frac{0}{200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4000)+4000}{2*100}=\frac{8000}{200}
=40
$