50=3x(20-x)

Solution for 50=3x(20-x) equation:

50=3x(20-x)

We move all terms to the left:

50-(3x(20-x))=0

We add all the numbers together, and all the variables

-(3x(-1x+20))+50=0


We calculate terms in parentheses: -(3x(-1x+20)), so:

3x(-1x+20)

We multiply parentheses

-3x^2+60x

Back to the equation:

-(-3x^2+60x)


We get rid of parentheses

3x^2-60x+50=0

a = 3; b = -60; c = +50;
Δ = b2-4ac
Δ = -602-4·3·50
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10\sqrt{30}}{2*3}=\frac{60-10\sqrt{30}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10\sqrt{30}}{2*3}=\frac{60+10\sqrt{30}}{6}
$