8y^2-40=6

Solution for 8y^2-40=6 equation:

8y^2-40=6

We move all terms to the left:

8y^2-40-(6)=0

We add all the numbers together, and all the variables

8y^2-46=0

a = 8; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·8·(-46)
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{23}}{2*8}=\frac{0-8\sqrt{23}}{16}
=-\frac{8\sqrt{23}}{16}
=-\frac{\sqrt{23}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{23}}{2*8}=\frac{0+8\sqrt{23}}{16}
=\frac{8\sqrt{23}}{16}
=\frac{\sqrt{23}}{2}
$