2h^2+4h=31

Solution for 2h^2+4h=31 equation:

2h^2+4h=31

We move all terms to the left:

2h^2+4h-(31)=0

a = 2; b = 4; c = -31;
Δ = b2-4ac
Δ = 42-4·2·(-31)
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{66}}{2*2}=\frac{-4-2\sqrt{66}}{4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{66}}{2*2}=\frac{-4+2\sqrt{66}}{4}
$