8-7/10h=6-1/3h

Solution for 8-7/10h=6-1/3h equation:

8-7/10h=6-1/3h

We move all terms to the left:

8-7/10h-(6-1/3h)=0


Domain of the equation: 10h!=0

h!=0/10

h!=0

h∈R



Domain of the equation: 3h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

-7/10h-(-1/3h+6)+8=0

We get rid of parentheses

-7/10h+1/3h-6+8=0

We calculate fractions


(-21h)/30h^2+10h/30h^2-6+8=0

We add all the numbers together, and all the variables

(-21h)/30h^2+10h/30h^2+2=0

We multiply all the terms by the denominator


(-21h)+10h+2*30h^2=0

We add all the numbers together, and all the variables

10h+(-21h)+2*30h^2=0

Wy multiply elements

60h^2+10h+(-21h)=0

We get rid of parentheses

60h^2+10h-21h=0

We add all the numbers together, and all the variables

60h^2-11h=0

a = 60; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·60·0
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*60}=\frac{0}{120}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*60}=\frac{22}{120}
=11/60
$