1/4h+1/2h+1/4+4=8

Solution for 1/4h+1/2h+1/4+4=8 equation:

1/4h+1/2h+1/4+4=8

We move all terms to the left:

1/4h+1/2h+1/4+4-(8)=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R



Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R


determiningTheFunctionDomain
1/4h+1/2h+4-8+1/4=0

We add all the numbers together, and all the variables

1/4h+1/2h-4+1/4=0

We calculate fractions


2h/128h^2+64h/128h^2+2h/128h^2-4=0

We multiply all the terms by the denominator


2h+64h+2h-4*128h^2=0

We add all the numbers together, and all the variables

68h-4*128h^2=0

Wy multiply elements

-512h^2+68h=0

a = -512; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-512)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-512}=\frac{-136}{-1024}
=17/128
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-512}=\frac{0}{-1024}
=0
$