-x^2=-162

Solution for -x^2=-162 equation:

-x^2=-162

We move all terms to the left:

-x^2-(-162)=0

We add all the numbers together, and all the variables

-1x^2+162=0

a = -1; b = 0; c = +162;
Δ = b2-4ac
Δ = 02-4·(-1)·162
Δ = 648
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*-1}=\frac{0-18\sqrt{2}}{-2}
=-\frac{18\sqrt{2}}{-2}
=-\frac{9\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*-1}=\frac{0+18\sqrt{2}}{-2}
=\frac{18\sqrt{2}}{-2}
=\frac{9\sqrt{2}}{-1}
$