2n^2-7n=400

Solution for 2n^2-7n=400 equation:

2n^2-7n=400

We move all terms to the left:

2n^2-7n-(400)=0

a = 2; b = -7; c = -400;
Δ = b2-4ac
Δ = -72-4·2·(-400)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-57}{2*2}=\frac{-50}{4}
=-12+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+57}{2*2}=\frac{64}{4}
=16
$