7n^2+40n-6=6

Solution for 7n^2+40n-6=6 equation:

7n^2+40n-6=6

We move all terms to the left:

7n^2+40n-6-(6)=0

We add all the numbers together, and all the variables

7n^2+40n-12=0

a = 7; b = 40; c = -12;
Δ = b2-4ac
Δ = 402-4·7·(-12)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-44}{2*7}=\frac{-84}{14}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+44}{2*7}=\frac{4}{14}
=2/7
$