N=40(m+7);m

Solution for N=40(m+7);m equation:

=40(N+7)N

We move all terms to the left:

-(40(N+7)N)=0


We calculate terms in parentheses: -(40(N+7)N), so:

40(N+7)N

We multiply parentheses

40N^2+280N

Back to the equation:

-(40N^2+280N)


We get rid of parentheses

-40N^2-280N=0

a = -40; b = -280; c = 0;
Δ = b2-4ac
Δ = -2802-4·(-40)·0
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-280}{2*-40}=\frac{0}{-80}
=0
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+280}{2*-40}=\frac{560}{-80}
=-7
$