7n(n+2)=5n+20

Solution for 7n(n+2)=5n+20 equation:

7n(n+2)=5n+20

We move all terms to the left:

7n(n+2)-(5n+20)=0

We multiply parentheses

7n^2+14n-(5n+20)=0

We get rid of parentheses

7n^2+14n-5n-20=0

We add all the numbers together, and all the variables

7n^2+9n-20=0

a = 7; b = 9; c = -20;
Δ = b2-4ac
Δ = 92-4·7·(-20)
Δ = 641
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{-(9)-\sqrt{641}}{2*7}=\frac{-9-\sqrt{641}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{641}}{2*7}=\frac{-9+\sqrt{641}}{14}
$