(69l+161)(46-23l)=0

Solution for (69l+161)(46-23l)=0 equation:

(69l+161)(46-23l)=0

We add all the numbers together, and all the variables

(69l+161)(-23l+46)=0

We multiply parentheses ..

(-1587l^2+3174l-3703l+7406)=0

We get rid of parentheses

-1587l^2+3174l-3703l+7406=0

We add all the numbers together, and all the variables

-1587l^2-529l+7406=0

a = -1587; b = -529; c = +7406;
Δ = b2-4ac
Δ = -5292-4·(-1587)·7406
Δ = 47293129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{47293129}=6877$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-529)-6877}{2*-1587}=\frac{-6348}{-3174}
=+2
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-529)+6877}{2*-1587}=\frac{7406}{-3174}
=-2+1/3
$