6n^2+17=1553

Solution for 6n^2+17=1553 equation:

6n^2+17=1553

We move all terms to the left:

6n^2+17-(1553)=0

We add all the numbers together, and all the variables

6n^2-1536=0

a = 6; b = 0; c = -1536;
Δ = b2-4ac
Δ = 02-4·6·(-1536)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-192}{2*6}=\frac{-192}{12}
=-16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+192}{2*6}=\frac{192}{12}
=16
$