7n^2+280=91n

Solution for 7n^2+280=91n equation:

7n^2+280=91n

We move all terms to the left:

7n^2+280-(91n)=0

a = 7; b = -91; c = +280;
Δ = b2-4ac
Δ = -912-4·7·280
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-21}{2*7}=\frac{70}{14}
=5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+21}{2*7}=\frac{112}{14}
=8
$