9n^2-7n=27048

Solution for 9n^2-7n=27048 equation:

9n^2-7n=27048

We move all terms to the left:

9n^2-7n-(27048)=0

a = 9; b = -7; c = -27048;
Δ = b2-4ac
Δ = -72-4·9·(-27048)
Δ = 973777
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:

$\sqrt{\Delta}=\sqrt{973777}=\sqrt{49*19873}=\sqrt{49}*\sqrt{19873}=7\sqrt{19873}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7\sqrt{19873}}{2*9}=\frac{7-7\sqrt{19873}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7\sqrt{19873}}{2*9}=\frac{7+7\sqrt{19873}}{18}
$