y^2=5/9

Solution for y^2=5/9 equation:

y^2=5/9

We move all terms to the left:

y^2-(5/9)=0

We add all the numbers together, and all the variables

y^2-(+5/9)=0

We get rid of parentheses

y^2-5/9=0

We multiply all the terms by the denominator


y^2*9-5=0

Wy multiply elements

9y^2-5=0

a = 9; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·9·(-5)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*9}=\frac{0-6\sqrt{5}}{18}
=-\frac{6\sqrt{5}}{18}
=-\frac{\sqrt{5}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*9}=\frac{0+6\sqrt{5}}{18}
=\frac{6\sqrt{5}}{18}
=\frac{\sqrt{5}}{3}
$