7000=5400+300n+50n^2

Solution for 7000=5400+300n+50n^2 equation:

7000=5400+300n+50n^2

We move all terms to the left:

7000-(5400+300n+50n^2)=0

We get rid of parentheses

-50n^2-300n-5400+7000=0

We add all the numbers together, and all the variables

-50n^2-300n+1600=0

a = -50; b = -300; c = +1600;
Δ = b2-4ac
Δ = -3002-4·(-50)·1600
Δ = 410000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{410000}=\sqrt{10000*41}=\sqrt{10000}*\sqrt{41}=100\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-100\sqrt{41}}{2*-50}=\frac{300-100\sqrt{41}}{-100}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+100\sqrt{41}}{2*-50}=\frac{300+100\sqrt{41}}{-100}
$