1/2h+1=3/4h+4

Solution for 1/2h+1=3/4h+4 equation:

1/2h+1=3/4h+4

We move all terms to the left:

1/2h+1-(3/4h+4)=0


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 4h+4)!=0

h∈R


We get rid of parentheses

1/2h-3/4h-4+1=0

We calculate fractions


4h/8h^2+(-6h)/8h^2-4+1=0

We add all the numbers together, and all the variables

4h/8h^2+(-6h)/8h^2-3=0

We multiply all the terms by the denominator


4h+(-6h)-3*8h^2=0

Wy multiply elements

-24h^2+4h+(-6h)=0

We get rid of parentheses

-24h^2+4h-6h=0

We add all the numbers together, and all the variables

-24h^2-2h=0

a = -24; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-24)·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*-24}=\frac{0}{-48}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-24}=\frac{4}{-48}
=-1/12
$