4n^2+4n=420

Solution for 4n^2+4n=420 equation:

4n^2+4n=420

We move all terms to the left:

4n^2+4n-(420)=0

a = 4; b = 4; c = -420;
Δ = b2-4ac
Δ = 42-4·4·(-420)
Δ = 6736
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:

$\sqrt{\Delta}=\sqrt{6736}=\sqrt{16*421}=\sqrt{16}*\sqrt{421}=4\sqrt{421}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{421}}{2*4}=\frac{-4-4\sqrt{421}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{421}}{2*4}=\frac{-4+4\sqrt{421}}{8}
$