6-1/5h=8-7/10h

Solution for 6-1/5h=8-7/10h equation:

6-1/5h=8-7/10h

We move all terms to the left:

6-1/5h-(8-7/10h)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R



Domain of the equation: 10h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

-1/5h-(-7/10h+8)+6=0

We get rid of parentheses

-1/5h+7/10h-8+6=0

We calculate fractions


(-10h)/50h^2+35h/50h^2-8+6=0

We add all the numbers together, and all the variables

(-10h)/50h^2+35h/50h^2-2=0

We multiply all the terms by the denominator


(-10h)+35h-2*50h^2=0

We add all the numbers together, and all the variables

35h+(-10h)-2*50h^2=0

Wy multiply elements

-100h^2+35h+(-10h)=0

We get rid of parentheses

-100h^2+35h-10h=0

We add all the numbers together, and all the variables

-100h^2+25h=0

a = -100; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-100)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-100}=\frac{-50}{-200}
=1/4
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-100}=\frac{0}{-200}
=0
$