1/16*y^2=81

Solution for 1/16*y^2=81 equation:

1/16y^2=81

We move all terms to the left:

1/16y^2-(81)=0


Domain of the equation: 16y^2!=0

y^2!=0/16

y^2!=√0

y!=0

y∈R


We multiply all the terms by the denominator


-81*16y^2+1=0

Wy multiply elements

-1296y^2+1=0

a = -1296; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1296)·1
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*-1296}=\frac{-72}{-2592}
=1/36
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*-1296}=\frac{72}{-2592}
=-1/36
$