-2h^2-24h=-82

Solution for -2h^2-24h=-82 equation:

-2h^2-24h=-82

We move all terms to the left:

-2h^2-24h-(-82)=0

We add all the numbers together, and all the variables

-2h^2-24h+82=0

a = -2; b = -24; c = +82;
Δ = b2-4ac
Δ = -242-4·(-2)·82
Δ = 1232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{77}}{2*-2}=\frac{24-4\sqrt{77}}{-4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{77}}{2*-2}=\frac{24+4\sqrt{77}}{-4}
$