2h-3=3/2h

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

2h-3=3/2h

We move all terms to the left:

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


Domain of the equation: 2h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2h-3/2h-3=0

We multiply all the terms by the denominator


2h*2h-3*2h-3=0

Wy multiply elements

4h^2-6h-3=0

a = 4; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·4·(-3)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*4}=\frac{6-2\sqrt{21}}{8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*4}=\frac{6+2\sqrt{21}}{8}
$