7n-4n(n+5)+12=6

Solution for 7n-4n(n+5)+12=6 equation:

7n-4n(n+5)+12=6

We move all terms to the left:

7n-4n(n+5)+12-(6)=0

We add all the numbers together, and all the variables

7n-4n(n+5)+6=0

We multiply parentheses

-4n^2+7n-20n+6=0

We add all the numbers together, and all the variables

-4n^2-13n+6=0

a = -4; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·(-4)·6
Δ = 265
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{-(-13)-\sqrt{265}}{2*-4}=\frac{13-\sqrt{265}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{265}}{2*-4}=\frac{13+\sqrt{265}}{-8}
$