7n^2=12+40n

Solution for 7n^2=12+40n equation:

7n^2=12+40n

We move all terms to the left:

7n^2-(12+40n)=0

We add all the numbers together, and all the variables

7n^2-(40n+12)=0

We get rid of parentheses

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