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

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

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

We move all terms to the left:

8-7/10h-(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+14=0

We multiply all the terms by the denominator


(-35h)+(-10h)+14*50h^2=0

Wy multiply elements

700h^2+(-35h)+(-10h)=0

We get rid of parentheses

700h^2-35h-10h=0

We add all the numbers together, and all the variables

700h^2-45h=0

a = 700; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·700·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*700}=\frac{0}{1400}
=0
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*700}=\frac{90}{1400}
=9/140
$