l+120/l=23

Solution for l+120/l=23 equation:

l+120/l=23

We move all terms to the left:

l+120/l-(23)=0


Domain of the equation: l!=0

l∈R


We multiply all the terms by the denominator


l*l-23*l+120=0

We add all the numbers together, and all the variables

-23l+l*l+120=0

Wy multiply elements

l^2-23l+120=0

a = 1; b = -23; c = +120;
Δ = b2-4ac
Δ = -232-4·1·120
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7}{2*1}=\frac{16}{2}
=8
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*1}=\frac{30}{2}
=15
$