4(n^2-1n-42)=0

Solution for 4(n^2-1n-42)=0 equation:

4(n^2-1n-42)=0

We multiply parentheses

4n^2-4n-168=0

a = 4; b = -4; c = -168;
Δ = b2-4ac
Δ = -42-4·4·(-168)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-52}{2*4}=\frac{-48}{8}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+52}{2*4}=\frac{56}{8}
=7
$