(5+3n)(2n+2)=240

Solution for (5+3n)(2n+2)=240 equation:

(5+3n)(2n+2)=240

We move all terms to the left:

(5+3n)(2n+2)-(240)=0

We add all the numbers together, and all the variables

(3n+5)(2n+2)-240=0

We multiply parentheses ..

(+6n^2+6n+10n+10)-240=0

We get rid of parentheses

6n^2+6n+10n+10-240=0

We add all the numbers together, and all the variables

6n^2+16n-230=0

a = 6; b = 16; c = -230;
Δ = b2-4ac
Δ = 162-4·6·(-230)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-76}{2*6}=\frac{-92}{12}
=-7+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+76}{2*6}=\frac{60}{12}
=5
$