n^2+11n+7n+28=0

Solution for n^2+11n+7n+28=0 equation:

n^2+11n+7n+28=0

We add all the numbers together, and all the variables

n^2+18n+28=0

a = 1; b = 18; c = +28;
Δ = b2-4ac
Δ = 182-4·1·28
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{53}}{2*1}=\frac{-18-2\sqrt{53}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{53}}{2*1}=\frac{-18+2\sqrt{53}}{2}
$