7n^2+41n-54=2

Solution for 7n^2+41n-54=2 equation:

7n^2+41n-54=2

We move all terms to the left:

7n^2+41n-54-(2)=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{-98}{14}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+57}{2*7}=\frac{16}{14}
=1+1/7
$