8n^2-53n-17=4

Solution for 8n^2-53n-17=4 equation:

8n^2-53n-17=4

We move all terms to the left:

8n^2-53n-17-(4)=0

We add all the numbers together, and all the variables

8n^2-53n-21=0

a = 8; b = -53; c = -21;
Δ = b2-4ac
Δ = -532-4·8·(-21)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-59}{2*8}=\frac{-6}{16}
=-3/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+59}{2*8}=\frac{112}{16}
=7
$