(3n+5)(2n+7)=44

Solution for (3n+5)(2n+7)=44 equation:

(3n+5)(2n+7)=44

We move all terms to the left:

(3n+5)(2n+7)-(44)=0

We multiply parentheses ..

(+6n^2+21n+10n+35)-44=0

We get rid of parentheses

6n^2+21n+10n+35-44=0

We add all the numbers together, and all the variables

6n^2+31n-9=0

a = 6; b = 31; c = -9;
Δ = b2-4ac
Δ = 312-4·6·(-9)
Δ = 1177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{1177}}{2*6}=\frac{-31-\sqrt{1177}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1177}}{2*6}=\frac{-31+\sqrt{1177}}{12}
$