2n(n=7)

Solution for 2n(n=7) equation:

2n(n=7)

We move all terms to the left:

2n(n-(7))=0

We multiply parentheses

2n^2-14n=0

a = 2; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·2·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*2}=\frac{28}{4}
=7
$