7n2-6n-14=21

Solution for 7n2-6n-14=21 equation:

7n^2-6n-14=21

We move all terms to the left:

7n^2-6n-14-(21)=0

We add all the numbers together, and all the variables

7n^2-6n-35=0

a = 7; b = -6; c = -35;
Δ = b2-4ac
Δ = -62-4·7·(-35)
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{254}}{2*7}=\frac{6-2\sqrt{254}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{254}}{2*7}=\frac{6+2\sqrt{254}}{14}
$