81w2+6=42

Solution for 81w2+6=42 equation:

81w^2+6=42

We move all terms to the left:

81w^2+6-(42)=0

We add all the numbers together, and all the variables

81w^2-36=0

a = 81; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·81·(-36)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108}{2*81}=\frac{-108}{162}
=-2/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108}{2*81}=\frac{108}{162}
=2/3
$