7n2=14n+21

Solution for 7n2=14n+21 equation:

7n^2=14n+21

We move all terms to the left:

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

We get rid of parentheses

7n^2-14n-21=0

a = 7; b = -14; c = -21;
Δ = b2-4ac
Δ = -142-4·7·(-21)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-28}{2*7}=\frac{-14}{14}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+28}{2*7}=\frac{42}{14}
=3
$