l(l+3)=238

Solution for l(l+3)=238 equation:

l(l+3)=238

We move all terms to the left:

l(l+3)-(238)=0

We multiply parentheses

l^2+3l-238=0

a = 1; b = 3; c = -238;
Δ = b2-4ac
Δ = 32-4·1·(-238)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-31}{2*1}=\frac{-34}{2}
=-17
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+31}{2*1}=\frac{28}{2}
=14
$