7n^2-34n-2=3

Solution for 7n^2-34n-2=3 equation:

7n^2-34n-2=3

We move all terms to the left:

7n^2-34n-2-(3)=0

We add all the numbers together, and all the variables

7n^2-34n-5=0

a = 7; b = -34; c = -5;
Δ = b2-4ac
Δ = -342-4·7·(-5)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-36}{2*7}=\frac{-2}{14}
=-1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+36}{2*7}=\frac{70}{14}
=5
$