6n(n-1)+4=40

Solution for 6n(n-1)+4=40 equation:

6n(n-1)+4=40

We move all terms to the left:

6n(n-1)+4-(40)=0

We add all the numbers together, and all the variables

6n(n-1)-36=0

We multiply parentheses

6n^2-6n-36=0

a = 6; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·6·(-36)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*6}=\frac{-24}{12}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*6}=\frac{36}{12}
=3
$