7n^2=-2n+16

Solution for 7n^2=-2n+16 equation:

7n^2=-2n+16

We move all terms to the left:

7n^2-(-2n+16)=0

We get rid of parentheses

7n^2+2n-16=0

a = 7; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·7·(-16)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{113}}{2*7}=\frac{-2-2\sqrt{113}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{113}}{2*7}=\frac{-2+2\sqrt{113}}{14}
$