-x^2=-67

Solution for -x^2=-67 equation:

-x^2=-67

We move all terms to the left:

-x^2-(-67)=0

We add all the numbers together, and all the variables

-1x^2+67=0

a = -1; b = 0; c = +67;
Δ = b2-4ac
Δ = 02-4·(-1)·67
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{67}}{2*-1}=\frac{0-2\sqrt{67}}{-2}
=-\frac{2\sqrt{67}}{-2}
=-\frac{\sqrt{67}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{67}}{2*-1}=\frac{0+2\sqrt{67}}{-2}
=\frac{2\sqrt{67}}{-2}
=\frac{\sqrt{67}}{-1}
$