2l^2-2l-3000=0

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

2l^2-2l-3000=0

a = 2; b = -2; c = -3000;
Δ = b2-4ac
Δ = -22-4·2·(-3000)
Δ = 24004
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:

$\sqrt{\Delta}=\sqrt{24004}=\sqrt{4*6001}=\sqrt{4}*\sqrt{6001}=2\sqrt{6001}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6001}}{2*2}=\frac{2-2\sqrt{6001}}{4}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6001}}{2*2}=\frac{2+2\sqrt{6001}}{4}
$