2y^2+18y+6=8

Solution for 2y^2+18y+6=8 equation:

2y^2+18y+6=8

We move all terms to the left:

2y^2+18y+6-(8)=0

We add all the numbers together, and all the variables

2y^2+18y-2=0

a = 2; b = 18; c = -2;
Δ = b2-4ac
Δ = 182-4·2·(-2)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{85}}{2*2}=\frac{-18-2\sqrt{85}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{85}}{2*2}=\frac{-18+2\sqrt{85}}{4}
$