7n^2=-24n+16

Solution for 7n^2=-24n+16 equation:

7n^2=-24n+16

We move all terms to the left:

7n^2-(-24n+16)=0

We get rid of parentheses

7n^2+24n-16=0

a = 7; b = 24; c = -16;
Δ = b2-4ac
Δ = 242-4·7·(-16)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-32}{2*7}=\frac{-56}{14}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+32}{2*7}=\frac{8}{14}
=4/7
$