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

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

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

We move all terms to the left:

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


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 4h-3)!=0

h∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

8h^2+4h-6h=0

We add all the numbers together, and all the variables

8h^2-2h=0

a = 8; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·8·0
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*8}=\frac{0}{16}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*8}=\frac{4}{16}
=1/4
$