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

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

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

We move all terms to the left:

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


Domain of the equation: 10h!=0

h!=0/10

h!=0

h∈R



Domain of the equation: 5h-6)!=0

h∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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
$