50x(15-x)=120

Solution for 50x(15-x)=120 equation:

50x(15-x)=120

We move all terms to the left:

50x(15-x)-(120)=0

We add all the numbers together, and all the variables

50x(-1x+15)-120=0

We multiply parentheses

-50x^2+750x-120=0

a = -50; b = 750; c = -120;
Δ = b2-4ac
Δ = 7502-4·(-50)·(-120)
Δ = 538500
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:

$\sqrt{\Delta}=\sqrt{538500}=\sqrt{100*5385}=\sqrt{100}*\sqrt{5385}=10\sqrt{5385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(750)-10\sqrt{5385}}{2*-50}=\frac{-750-10\sqrt{5385}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(750)+10\sqrt{5385}}{2*-50}=\frac{-750+10\sqrt{5385}}{-100}
$