Answer
The solutions are $\frac{-9}{2}$ and $\frac{9}{2}$.
Work Step by Step
4$y^{2}$-81=0
$(2y)^{2}$-$9^{2}$=0
(2y+9)(2y-9)=0
2y+9 =0 or 2y-9=0
2y+9-9 =0 -9 or 2y-9+9=0+9
2y=-9 or 2y=9
$\frac{2y}{2}$=$\frac{-9}{2}$ or $\frac{2y}{2}$=$\frac{9}{2}$
y=$\frac{-9}{2}$ or y= $\frac{9}{2}$
The solutions are $\frac{-9}{2}$ and $\frac{9}{2}$.
Check
Let x= $\frac{-9}{2}$
4$y^{2}$-81=0
4$(-9/2)^{2}$-81=0
4*$\frac{81}{4}$-$\frac{324}{4}$=0
$\frac{324}{4}$-$\frac{324}{4}$=0
0=0
Let x= $\frac{9}{2}$
4$y^{2}$-81=0
4$(9/2)^{2}$-81=0
4*$\frac{81}{4}$-$\frac{324}{4}$=0
$\frac{324}{4}$-$\frac{324}{4}$=0
0=0
