8y^2=82

Solution for 8y^2=82 equation:

8y^2=82

We move all terms to the left:

8y^2-(82)=0

a = 8; b = 0; c = -82;
Δ = b2-4ac
Δ = 02-4·8·(-82)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{41}}{2*8}=\frac{0-8\sqrt{41}}{16}
=-\frac{8\sqrt{41}}{16}
=-\frac{\sqrt{41}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{41}}{2*8}=\frac{0+8\sqrt{41}}{16}
=\frac{8\sqrt{41}}{16}
=\frac{\sqrt{41}}{2}
$