2(h2+3)-2h=34

Solution for 2(h2+3)-2h=34 equation:

2(h2+3)-2h=34

We move all terms to the left:

2(h2+3)-2h-(34)=0

We add all the numbers together, and all the variables

2(+h^2+3)-2h-34=0

We multiply parentheses

2h^2-2h+6-34=0

We add all the numbers together, and all the variables

2h^2-2h-28=0

a = 2; b = -2; c = -28;
Δ = b2-4ac
Δ = -22-4·2·(-28)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{57}}{2*2}=\frac{2-2\sqrt{57}}{4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{57}}{2*2}=\frac{2+2\sqrt{57}}{4}
$