2(l^2-l-3000)=0

Solution for 2(l^2-l-3000)=0 equation:

2(l^2-l-3000)=0

We multiply parentheses

2l^2-2l-6000=0

a = 2; b = -2; c = -6000;
Δ = b2-4ac
Δ = -22-4·2·(-6000)
Δ = 48004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48004}=\sqrt{4*12001}=\sqrt{4}*\sqrt{12001}=2\sqrt{12001}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{12001}}{2*2}=\frac{2-2\sqrt{12001}}{4}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{12001}}{2*2}=\frac{2+2\sqrt{12001}}{4}
$