7n^2=6n+21

Solution for 7n^2=6n+21 equation:

7n^2=6n+21

We move all terms to the left:

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

We get rid of parentheses

7n^2-6n-21=0

a = 7; b = -6; c = -21;
Δ = b2-4ac
Δ = -62-4·7·(-21)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{39}}{2*7}=\frac{6-4\sqrt{39}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{39}}{2*7}=\frac{6+4\sqrt{39}}{14}
$