17=1/2h^2

Solution for 17=1/2h^2 equation:

17=1/2h^2

We move all terms to the left:

17-(1/2h^2)=0


Domain of the equation: 2h^2)!=0

h!=0/1

h!=0

h∈R


We get rid of parentheses

-1/2h^2+17=0

We multiply all the terms by the denominator


17*2h^2-1=0

Wy multiply elements

34h^2-1=0

a = 34; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·34·(-1)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{34}}{2*34}=\frac{0-2\sqrt{34}}{68}
=-\frac{2\sqrt{34}}{68}
=-\frac{\sqrt{34}}{34}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{34}}{2*34}=\frac{0+2\sqrt{34}}{68}
=\frac{2\sqrt{34}}{68}
=\frac{\sqrt{34}}{34}
$