3/4h+9=1/2h+8

Solution for 3/4h+9=1/2h+8 equation:

3/4h+9=1/2h+8

We move all terms to the left:

3/4h+9-(1/2h+8)=0


Domain of the equation: 4h!=0

h!=0/4

h!=0

h∈R



Domain of the equation: 2h+8)!=0

h∈R


We get rid of parentheses

3/4h-1/2h-8+9=0

We calculate fractions


6h/8h^2+(-4h)/8h^2-8+9=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

8h^2+6h-4h=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{-4}{16}
=-1/4
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*8}=\frac{0}{16}
=0
$