2(n-3)(n+7)=2n

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

2(n-3)(n+7)=2n

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

2(+n^2+7n-3n-21)-2n=0

We multiply parentheses

2n^2+14n-6n-2n-42=0

We add all the numbers together, and all the variables

2n^2+6n-42=0

a = 2; b = 6; c = -42;
Δ = b2-4ac
Δ = 62-4·2·(-42)
Δ = 372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{93}}{2*2}=\frac{-6-2\sqrt{93}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{93}}{2*2}=\frac{-6+2\sqrt{93}}{4}
$