2y^2+8y=34

Solution for 2y^2+8y=34 equation:

2y^2+8y=34

We move all terms to the left:

2y^2+8y-(34)=0

a = 2; b = 8; c = -34;
Δ = b2-4ac
Δ = 82-4·2·(-34)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{21}}{2*2}=\frac{-8-4\sqrt{21}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{21}}{2*2}=\frac{-8+4\sqrt{21}}{4}
$