-2x^2=-41

Solution for -2x^2=-41 equation:

-2x^2=-41

We move all terms to the left:

-2x^2-(-41)=0

We add all the numbers together, and all the variables

-2x^2+41=0

a = -2; b = 0; c = +41;
Δ = b2-4ac
Δ = 02-4·(-2)·41
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{82}}{2*-2}=\frac{0-2\sqrt{82}}{-4}
=-\frac{2\sqrt{82}}{-4}
=-\frac{\sqrt{82}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{82}}{2*-2}=\frac{0+2\sqrt{82}}{-4}
=\frac{2\sqrt{82}}{-4}
=\frac{\sqrt{82}}{-2}
$