2l^2-4l-111=0

Solution for 2l^2-4l-111=0 equation:

2l^2-4l-111=0

a = 2; b = -4; c = -111;
Δ = b2-4ac
Δ = -42-4·2·(-111)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{226}}{2*2}=\frac{4-2\sqrt{226}}{4}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{226}}{2*2}=\frac{4+2\sqrt{226}}{4}
$