7n^2=-168+77n

Solution for 7n^2=-168+77n equation:

7n^2=-168+77n

We move all terms to the left:

7n^2-(-168+77n)=0

We add all the numbers together, and all the variables

7n^2-(77n-168)=0

We get rid of parentheses

7n^2-77n+168=0

a = 7; b = -77; c = +168;
Δ = b2-4ac
Δ = -772-4·7·168
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-35}{2*7}=\frac{42}{14}
=3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+35}{2*7}=\frac{112}{14}
=8
$