2g^2+56g+50=0

Solution for 2g^2+56g+50=0 equation:

2g^2+56g+50=0

a = 2; b = 56; c = +50;
Δ = b2-4ac
Δ = 562-4·2·50
Δ = 2736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-12\sqrt{19}}{2*2}=\frac{-56-12\sqrt{19}}{4}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+12\sqrt{19}}{2*2}=\frac{-56+12\sqrt{19}}{4}
$