-4x^2=-82

Solution for -4x^2=-82 equation:

-4x^2=-82

We move all terms to the left:

-4x^2-(-82)=0

We add all the numbers together, and all the variables

-4x^2+82=0

a = -4; b = 0; c = +82;
Δ = b2-4ac
Δ = 02-4·(-4)·82
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{82}}{2*-4}=\frac{0-4\sqrt{82}}{-8}
=-\frac{4\sqrt{82}}{-8}
=-\frac{\sqrt{82}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{82}}{2*-4}=\frac{0+4\sqrt{82}}{-8}
=\frac{4\sqrt{82}}{-8}
=\frac{\sqrt{82}}{-2}
$