81*9^2b-2=27

Solution for 81*9^2b-2=27 equation:

81*9^2b-2=27

We move all terms to the left:

81*9^2b-2-(27)=0

We add all the numbers together, and all the variables

81*9^2b-29=0

Wy multiply elements

729b^2-29=0

a = 729; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·729·(-29)
Δ = 84564
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84564}=\sqrt{2916*29}=\sqrt{2916}*\sqrt{29}=54\sqrt{29}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{29}}{2*729}=\frac{0-54\sqrt{29}}{1458}
=-\frac{54\sqrt{29}}{1458}
=-\frac{\sqrt{29}}{27}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{29}}{2*729}=\frac{0+54\sqrt{29}}{1458}
=\frac{54\sqrt{29}}{1458}
=\frac{\sqrt{29}}{27}
$