8y^2+16y-82=0

Solution for 8y^2+16y-82=0 equation:

8y^2+16y-82=0

a = 8; b = 16; c = -82;
Δ = b2-4ac
Δ = 162-4·8·(-82)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24\sqrt{5}}{2*8}=\frac{-16-24\sqrt{5}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24\sqrt{5}}{2*8}=\frac{-16+24\sqrt{5}}{16}
$