7n^2-23n-17=3

Solution for 7n^2-23n-17=3 equation:

7n^2-23n-17=3

We move all terms to the left:

7n^2-23n-17-(3)=0

We add all the numbers together, and all the variables

7n^2-23n-20=0

a = 7; b = -23; c = -20;
Δ = b2-4ac
Δ = -232-4·7·(-20)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-33}{2*7}=\frac{-10}{14}
=-5/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+33}{2*7}=\frac{56}{14}
=4
$