4/5h+5=9/10h-1

Solution for 4/5h+5=9/10h-1 equation:

4/5h+5=9/10h-1

We move all terms to the left:

4/5h+5-(9/10h-1)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: 10h-1)!=0

h∈R


We get rid of parentheses

4/5h-9/10h+1+5=0

We calculate fractions


40h/50h^2+(-45h)/50h^2+1+5=0

We add all the numbers together, and all the variables

40h/50h^2+(-45h)/50h^2+6=0

We multiply all the terms by the denominator


40h+(-45h)+6*50h^2=0

Wy multiply elements

300h^2+40h+(-45h)=0

We get rid of parentheses

300h^2+40h-45h=0

We add all the numbers together, and all the variables

300h^2-5h=0

a = 300; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·300·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*300}=\frac{0}{600}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*300}=\frac{10}{600}
=1/60
$