(1/2)h-1=3/8

Solution for (1/2)h-1=3/8 equation:

(1/2)h-1=3/8

We move all terms to the left:

(1/2)h-1-(3/8)=0


Domain of the equation: 2)h!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

(+1/2)h-1-(+3/8)=0

We multiply parentheses

h^2-1-(+3/8)=0

We get rid of parentheses

h^2-1-3/8=0

We multiply all the terms by the denominator


h^2*8-3-1*8=0

We add all the numbers together, and all the variables

h^2*8-11=0

Wy multiply elements

8h^2-11=0

a = 8; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·8·(-11)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*8}=\frac{0-4\sqrt{22}}{16}
=-\frac{4\sqrt{22}}{16}
=-\frac{\sqrt{22}}{4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*8}=\frac{0+4\sqrt{22}}{16}
=\frac{4\sqrt{22}}{16}
=\frac{\sqrt{22}}{4}
$