1/2*h-16=5/8*h

Solution for 1/2*h-16=5/8*h equation:

1/2h-16=5/8h

We move all terms to the left:

1/2h-16-(5/8h)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 8h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

1/2h-(+5/8h)-16=0

We get rid of parentheses

1/2h-5/8h-16=0

We calculate fractions


8h/16h^2+(-10h)/16h^2-16=0

We multiply all the terms by the denominator


8h+(-10h)-16*16h^2=0

Wy multiply elements

-256h^2+8h+(-10h)=0

We get rid of parentheses

-256h^2+8h-10h=0

We add all the numbers together, and all the variables

-256h^2-2h=0

a = -256; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-256)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-256}=\frac{0}{-512}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-256}=\frac{4}{-512}
=-1/128
$