7n^2=8-55n

Solution for 7n^2=8-55n equation:

7n^2=8-55n

We move all terms to the left:

7n^2-(8-55n)=0

We add all the numbers together, and all the variables

7n^2-(-55n+8)=0

We get rid of parentheses

7n^2+55n-8=0

a = 7; b = 55; c = -8;
Δ = b2-4ac
Δ = 552-4·7·(-8)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-57}{2*7}=\frac{-112}{14}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+57}{2*7}=\frac{2}{14}
=1/7
$