n+7=7n^2+42n-49

Solution for n+7=7n^2+42n-49 equation:

n+7=7n^2+42n-49

We move all terms to the left:

n+7-(7n^2+42n-49)=0

We get rid of parentheses

-7n^2+n-42n+49+7=0

We add all the numbers together, and all the variables

-7n^2-41n+56=0

a = -7; b = -41; c = +56;
Δ = b2-4ac
Δ = -412-4·(-7)·56
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{-(-41)-57}{2*-7}=\frac{-16}{-14}
=1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+57}{2*-7}=\frac{98}{-14}
=-7
$