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

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

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

We move all terms to the left:

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


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


(4h+1)+2h-4*8h^2=0

We add all the numbers together, and all the variables

2h+(4h+1)-4*8h^2=0

Wy multiply elements

-32h^2+2h+(4h+1)=0

We get rid of parentheses

-32h^2+2h+4h+1=0

We add all the numbers together, and all the variables

-32h^2+6h+1=0

a = -32; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-32)·1
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{41}}{2*-32}=\frac{-6-2\sqrt{41}}{-64}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{41}}{2*-32}=\frac{-6+2\sqrt{41}}{-64}
$