1/5h+4=3/4h+8

Solution for 1/5h+4=3/4h+8 equation:

1/5h+4=3/4h+8

We move all terms to the left:

1/5h+4-(3/4h+8)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: 4h+8)!=0

h∈R


We get rid of parentheses

1/5h-3/4h-8+4=0

We calculate fractions


4h/20h^2+(-15h)/20h^2-8+4=0

We add all the numbers together, and all the variables

4h/20h^2+(-15h)/20h^2-4=0

We multiply all the terms by the denominator


4h+(-15h)-4*20h^2=0

Wy multiply elements

-80h^2+4h+(-15h)=0

We get rid of parentheses

-80h^2+4h-15h=0

We add all the numbers together, and all the variables

-80h^2-11h=0

a = -80; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-80)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-80}=\frac{0}{-160}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-80}=\frac{22}{-160}
=-11/80
$