81x2-144x+64=8

Solution for 81x2-144x+64=8 equation:

81x^2-144x+64=8

We move all terms to the left:

81x^2-144x+64-(8)=0

We add all the numbers together, and all the variables

81x^2-144x+56=0

a = 81; b = -144; c = +56;
Δ = b2-4ac
Δ = -1442-4·81·56
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-36\sqrt{2}}{2*81}=\frac{144-36\sqrt{2}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+36\sqrt{2}}{2*81}=\frac{144+36\sqrt{2}}{162}
$