(1/2)8h=58

Solution for (1/2)8h=58 equation:

(1/2)8h=58

We move all terms to the left:

(1/2)8h-(58)=0


Domain of the equation: 2)8h!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

(+1/2)8h-58=0

We multiply parentheses

8h^2-58=0

a = 8; b = 0; c = -58;
Δ = b2-4ac
Δ = 02-4·8·(-58)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{29}}{2*8}=\frac{0-8\sqrt{29}}{16}
=-\frac{8\sqrt{29}}{16}
=-\frac{\sqrt{29}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{29}}{2*8}=\frac{0+8\sqrt{29}}{16}
=\frac{8\sqrt{29}}{16}
=\frac{\sqrt{29}}{2}
$