3/5h-9=2/4h-1

Solution for 3/5h-9=2/4h-1 equation:

3/5h-9=2/4h-1

We move all terms to the left:

3/5h-9-(2/4h-1)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: 4h-1)!=0

h∈R


We get rid of parentheses

3/5h-2/4h+1-9=0

We calculate fractions


12h/20h^2+(-10h)/20h^2+1-9=0

We add all the numbers together, and all the variables

12h/20h^2+(-10h)/20h^2-8=0

We multiply all the terms by the denominator


12h+(-10h)-8*20h^2=0

Wy multiply elements

-160h^2+12h+(-10h)=0

We get rid of parentheses

-160h^2+12h-10h=0

We add all the numbers together, and all the variables

-160h^2+2h=0

a = -160; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-160)·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*-160}=\frac{-4}{-320}
=1/80
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-160}=\frac{0}{-320}
=0
$