7(4n2+17)=819

Solution for 7(4n2+17)=819 equation:

7(4n^2+17)=819

We move all terms to the left:

7(4n^2+17)-(819)=0

We multiply parentheses

28n^2+119-819=0

We add all the numbers together, and all the variables

28n^2-700=0

a = 28; b = 0; c = -700;
Δ = b2-4ac
Δ = 02-4·28·(-700)
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{-(0)-280}{2*28}=\frac{-280}{56}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+280}{2*28}=\frac{280}{56}
=5
$