(7n+9)(n+7)=47

Solution for (7n+9)(n+7)=47 equation:

(7n+9)(n+7)=47

We move all terms to the left:

(7n+9)(n+7)-(47)=0

We multiply parentheses ..

(+7n^2+49n+9n+63)-47=0

We get rid of parentheses

7n^2+49n+9n+63-47=0

We add all the numbers together, and all the variables

7n^2+58n+16=0

a = 7; b = 58; c = +16;
Δ = b2-4ac
Δ = 582-4·7·16
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-54}{2*7}=\frac{-112}{14}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+54}{2*7}=\frac{-4}{14}
=-2/7
$