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

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

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

We move all terms to the left:

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


Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R



Domain of the equation: 4h)!=0

h!=0/1

h!=0

h∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

10h-3*8h^2=0

Wy multiply elements

-24h^2+10h=0

a = -24; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-24)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-24}=\frac{-20}{-48}
=5/12
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-24}=\frac{0}{-48}
=0
$