6n^2+17=1193

Solution for 6n^2+17=1193 equation:

6n^2+17=1193

We move all terms to the left:

6n^2+17-(1193)=0

We add all the numbers together, and all the variables

6n^2-1176=0

a = 6; b = 0; c = -1176;
Δ = b2-4ac
Δ = 02-4·6·(-1176)
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-168}{2*6}=\frac{-168}{12}
=-14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+168}{2*6}=\frac{168}{12}
=14
$