1/2h+4=1/8h+88

Solution for 1/2h+4=1/8h+88 equation:

1/2h+4=1/8h+88

We move all terms to the left:

1/2h+4-(1/8h+88)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 8h+88)!=0

h∈R


We get rid of parentheses

1/2h-1/8h-88+4=0

We calculate fractions


8h/16h^2+(-2h)/16h^2-88+4=0

We add all the numbers together, and all the variables

8h/16h^2+(-2h)/16h^2-84=0

We multiply all the terms by the denominator


8h+(-2h)-84*16h^2=0

Wy multiply elements

-1344h^2+8h+(-2h)=0

We get rid of parentheses

-1344h^2+8h-2h=0

We add all the numbers together, and all the variables

-1344h^2+6h=0

a = -1344; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1344)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-1344}=\frac{-12}{-2688}
=1/224
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1344}=\frac{0}{-2688}
=0
$