8y^2-32y-10=0

Solution for 8y^2-32y-10=0 equation:

8y^2-32y-10=0

a = 8; b = -32; c = -10;
Δ = b2-4ac
Δ = -322-4·8·(-10)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{21}}{2*8}=\frac{32-8\sqrt{21}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{21}}{2*8}=\frac{32+8\sqrt{21}}{16}
$