8n^2-43n=30

Solution for 8n^2-43n=30 equation:

8n^2-43n=30

We move all terms to the left:

8n^2-43n-(30)=0

a = 8; b = -43; c = -30;
Δ = b2-4ac
Δ = -432-4·8·(-30)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-53}{2*8}=\frac{-10}{16}
=-5/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+53}{2*8}=\frac{96}{16}
=6
$