y^2=27/81

Solution for y^2=27/81 equation:

y^2=27/81

We move all terms to the left:

y^2-(27/81)=0

We add all the numbers together, and all the variables

y^2-(+27/81)=0

We get rid of parentheses

y^2-27/81=0

We multiply all the terms by the denominator


y^2*81-27=0

Wy multiply elements

81y^2-27=0

a = 81; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·81·(-27)
Δ = 8748
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8748}=\sqrt{2916*3}=\sqrt{2916}*\sqrt{3}=54\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{3}}{2*81}=\frac{0-54\sqrt{3}}{162}
=-\frac{54\sqrt{3}}{162}
=-\frac{\sqrt{3}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{3}}{2*81}=\frac{0+54\sqrt{3}}{162}
=\frac{54\sqrt{3}}{162}
=\frac{\sqrt{3}}{3}
$