12-8n^2=-1139

Solution for 12-8n^2=-1139 equation:

12-8n^2=-1139

We move all terms to the left:

12-8n^2-(-1139)=0

We add all the numbers together, and all the variables

-8n^2+1151=0

a = -8; b = 0; c = +1151;
Δ = b2-4ac
Δ = 02-4·(-8)·1151
Δ = 36832
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:

$\sqrt{\Delta}=\sqrt{36832}=\sqrt{16*2302}=\sqrt{16}*\sqrt{2302}=4\sqrt{2302}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2302}}{2*-8}=\frac{0-4\sqrt{2302}}{-16}
=-\frac{4\sqrt{2302}}{-16}
=-\frac{\sqrt{2302}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2302}}{2*-8}=\frac{0+4\sqrt{2302}}{-16}
=\frac{4\sqrt{2302}}{-16}
=\frac{\sqrt{2302}}{-4}
$