2l^2-2l-1500=0

Solution for 2l^2-2l-1500=0 equation:

2l^2-2l-1500=0

a = 2; b = -2; c = -1500;
Δ = b2-4ac
Δ = -22-4·2·(-1500)
Δ = 12004
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:

$\sqrt{\Delta}=\sqrt{12004}=\sqrt{4*3001}=\sqrt{4}*\sqrt{3001}=2\sqrt{3001}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3001}}{2*2}=\frac{2-2\sqrt{3001}}{4}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3001}}{2*2}=\frac{2+2\sqrt{3001}}{4}
$