l(l-3)=238^2

Solution for l(l-3)=238^2 equation:

l(l-3)=238^2

We move all terms to the left:

l(l-3)-(238^2)=0

We add all the numbers together, and all the variables

l(l-3)-56644=0

We multiply parentheses

l^2-3l-56644=0

a = 1; b = -3; c = -56644;
Δ = b2-4ac
Δ = -32-4·1·(-56644)
Δ = 226585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{226585}}{2*1}=\frac{3-\sqrt{226585}}{2}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{226585}}{2*1}=\frac{3+\sqrt{226585}}{2}
$