238=l(l+3)

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

238=l(l+3)

We move all terms to the left:

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


We calculate terms in parentheses: -(l(l+3)), so:

l(l+3)

We multiply parentheses

l^2+3l

Back to the equation:

-(l^2+3l)


We get rid of parentheses

-l^2-3l+238=0

We add all the numbers together, and all the variables

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