-10-9n^2=-163

Solution for -10-9n^2=-163 equation:

-10-9n^2=-163

We move all terms to the left:

-10-9n^2-(-163)=0

We add all the numbers together, and all the variables

-9n^2+153=0

a = -9; b = 0; c = +153;
Δ = b2-4ac
Δ = 02-4·(-9)·153
Δ = 5508
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:

$\sqrt{\Delta}=\sqrt{5508}=\sqrt{324*17}=\sqrt{324}*\sqrt{17}=18\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{17}}{2*-9}=\frac{0-18\sqrt{17}}{-18}
=-\frac{18\sqrt{17}}{-18}
=-\frac{\sqrt{17}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{17}}{2*-9}=\frac{0+18\sqrt{17}}{-18}
=\frac{18\sqrt{17}}{-18}
=\frac{\sqrt{17}}{-1}
$