2y^2+18y+37=0

Solution for 2y^2+18y+37=0 equation:

2y^2+18y+37=0

a = 2; b = 18; c = +37;
Δ = b2-4ac
Δ = 182-4·2·37
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{7}}{2*2}=\frac{-18-2\sqrt{7}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{7}}{2*2}=\frac{-18+2\sqrt{7}}{4}
$