30(15-x)20x=370

Solution for 30(15-x)20x=370 equation:

30(15-x)20x=370

We move all terms to the left:

30(15-x)20x-(370)=0

We add all the numbers together, and all the variables

30(-1x+15)20x-370=0

We multiply parentheses

-600x^2+9000x-370=0

a = -600; b = 9000; c = -370;
Δ = b2-4ac
Δ = 90002-4·(-600)·(-370)
Δ = 80112000
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:

$\sqrt{\Delta}=\sqrt{80112000}=\sqrt{1600*50070}=\sqrt{1600}*\sqrt{50070}=40\sqrt{50070}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9000)-40\sqrt{50070}}{2*-600}=\frac{-9000-40\sqrt{50070}}{-1200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9000)+40\sqrt{50070}}{2*-600}=\frac{-9000+40\sqrt{50070}}{-1200}
$