82(3^2x-4)-110=557

Solution for 82(3^2x-4)-110=557 equation:

82(3^2x-4)-110=557

We move all terms to the left:

82(3^2x-4)-110-(557)=0

We add all the numbers together, and all the variables

82(3^2x-4)-667=0

We multiply parentheses

246x^2-328-667=0

We add all the numbers together, and all the variables

246x^2-995=0

a = 246; b = 0; c = -995;
Δ = b2-4ac
Δ = 02-4·246·(-995)
Δ = 979080
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:

$\sqrt{\Delta}=\sqrt{979080}=\sqrt{4*244770}=\sqrt{4}*\sqrt{244770}=2\sqrt{244770}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{244770}}{2*246}=\frac{0-2\sqrt{244770}}{492}
=-\frac{2\sqrt{244770}}{492}
=-\frac{\sqrt{244770}}{246}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{244770}}{2*246}=\frac{0+2\sqrt{244770}}{492}
=\frac{2\sqrt{244770}}{492}
=\frac{\sqrt{244770}}{246}
$