4/20h+4=3/5h+8

Solution for 4/20h+4=3/5h+8 equation:

4/20h+4=3/5h+8

We move all terms to the left:

4/20h+4-(3/5h+8)=0


Domain of the equation: 20h!=0

h!=0/20

h!=0

h∈R



Domain of the equation: 5h+8)!=0

h∈R


We get rid of parentheses

4/20h-3/5h-8+4=0

We calculate fractions


20h/100h^2+(-60h)/100h^2-8+4=0

We add all the numbers together, and all the variables

20h/100h^2+(-60h)/100h^2-4=0

We multiply all the terms by the denominator


20h+(-60h)-4*100h^2=0

Wy multiply elements

-400h^2+20h+(-60h)=0

We get rid of parentheses

-400h^2+20h-60h=0

We add all the numbers together, and all the variables

-400h^2-40h=0

a = -400; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-400)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-400}=\frac{0}{-800}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-400}=\frac{80}{-800}
=-1/10
$