7n2-43n=-40

Solution for 7n2-43n=-40 equation:

7n^2-43n=-40

We move all terms to the left:

7n^2-43n-(-40)=0

We add all the numbers together, and all the variables

7n^2-43n+40=0

a = 7; b = -43; c = +40;
Δ = b2-4ac
Δ = -432-4·7·40
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-27}{2*7}=\frac{16}{14}
=1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+27}{2*7}=\frac{70}{14}
=5
$