9y^2-3=23

Solution for 9y^2-3=23 equation:

9y^2-3=23

We move all terms to the left:

9y^2-3-(23)=0

We add all the numbers together, and all the variables

9y^2-26=0

a = 9; b = 0; c = -26;
Δ = b2-4ac
Δ = 02-4·9·(-26)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{26}}{2*9}=\frac{0-6\sqrt{26}}{18}
=-\frac{6\sqrt{26}}{18}
=-\frac{\sqrt{26}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{26}}{2*9}=\frac{0+6\sqrt{26}}{18}
=\frac{6\sqrt{26}}{18}
=\frac{\sqrt{26}}{3}
$