2x(30-x)=300

Solution for 2x(30-x)=300 equation:

2x(30-x)=300

We move all terms to the left:

2x(30-x)-(300)=0

We add all the numbers together, and all the variables

2x(-1x+30)-300=0

We multiply parentheses

-2x^2+60x-300=0

a = -2; b = 60; c = -300;
Δ = b2-4ac
Δ = 602-4·(-2)·(-300)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{3}}{2*-2}=\frac{-60-20\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{3}}{2*-2}=\frac{-60+20\sqrt{3}}{-4}
$