7n^2-127n=420

Solution for 7n^2-127n=420 equation:

7n^2-127n=420

We move all terms to the left:

7n^2-127n-(420)=0

a = 7; b = -127; c = -420;
Δ = b2-4ac
Δ = -1272-4·7·(-420)
Δ = 27889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27889}=167$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-127)-167}{2*7}=\frac{-40}{14}
=-2+6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-127)+167}{2*7}=\frac{294}{14}
=21
$